Philosopher Edward Feser has argued on his blog that the prior probability of a miracle occurring has to do with our background knowledge of the world; therefore, there isn’t an absurdly low prior probability of a miracle occurring if: God exists, supernaturalism is true, God wants to perform miracles, God wants to raise Jesus from the dead, etc.
I don’t know what to label this objection, and I constantly see it trotted out in apologetic circles. And (at this point) I’m unaware of whether this objection is based on a strawman, ignorance, lies, all of the above, etc.
For one, atheist Michael Martin has argued that miracles are improbable even given the truth of theism and other assumptions. One of Michael Martin’s argument has to deal with God’s power. God has many ways to redeem mankind because God is all-powerful. Another argument that Martin gives has to do with the fact that even if miracles are possible, they are still extremely rare (frequency is actually an objective measure of probability). So, even if that doesn’t mean miracles are absurdly improbable, with respect to prior probability, that doesn’t mean miracles still aren’t really improbable (or just improbable). Also, it’s certainly not clear how God existing is even close to being sufficient to make the resurrection likely (with respect to prior probability). One could argue that an all-good and all-powerful Being would not raise Jesus, given many of the teachings of Jesus. Finally, one could also argue that it would be immoral of God to perform miracles. There are also other arguments as well, and they also do not reject supernaturalism/theism.
Secondly, there is no burden of proof for the skeptic when it comes to miracles. It’s up to the Christian theist to demonstrate that all the relevant background assumptions are in fact true. Thus, the skeptic isn’t engaging in circular reasoning (or ‘begging the question’) and any suggestions to the contrary are sophistry (i.e. an attempt to shift the burden of proof). If I want to demonstrate the truth of Y to you and the truth of Y requires the truth of X, then I also have to demonstrate the truth of X to you (if you don’t already accept the truth of X).
More Probable vs. Probable
When it comes to the story of the resurrection of Jesus, it’s not enough to point to the Gospels and claim that our supposed ‘evidence’ makes the resurrection hypothesis (i.e. God raised Jesus from the dead) more likely than it would have been otherwise (i.e. not having that evidence or ‘facts’). Instead, at a minimum, the Christian needs to establish that the resurrection hypothesis is probably true, and the resurrection hypothesis can’t be probable unless God exists. That’s because the resurrection hypothesis entails that God exists, because the resurrection hypothesis says, “God raised Jesus from the dead”; God can’t raise Jesus from the dead if God doesn’t exist. God raising Jesus is what has religious significance, and it is not very religiously significant if, for instance, aliens raised Jesus; it’s also not what Christians believe!
Why is it not enough to make the resurrection hypothesis just more probable? Because that’s not enough for a Christian to have outright belief in the resurrection, a fortiori, it won’t even be close to sufficient for convincing a skeptic. Hume was right that one needs to establish that a miracle probably happened. What that means is that the probability of a miracle occurring needs to be greater than 50%. Nevertheless, Hume likely was a little too lenient. Because, for example, it seems implausible that 51% confidence in a claim is enough for me to just believe in said claim [1].
Richard Swinburne is one of the only philosophers of religion that has even attempted to meet Hume’s challenge. Craig, Moreland, McGrew, and others have largely ignored trying to show that the resurrection of Jesus probably happened.
Notes
[1] This is according to contemporary epistemology. Suppose I think there is a 51% chance that there will be a tornado in my state tomorrow. Does that mean I believe this proposition? That doesn’t seem right. For one, 51% is barely above 50%; it’s basically a coin toss. Secondly, since confidence levels constantly fluctuate, 51% can easily change to 50% or 45% confidence (for instance).
Philosophy of Religion blog 
The minute one gets onto the subject of Jesus being raised (and in fact his whole existence) one has to question the entire background. Is the Creation story and the whole Original Sin idea that follows at all reasonable or feasible? Because, if that is the load of codswallop it seems, then whether or not Jesus existed, and whatever his doings and nature may have been, are of no importance whatsoever. It is necessary to buy into Eden to get entrance into Salvation. Dismiss the first and the second falls away. So do miracles and the whole hoo-ha.
Does he say what he thinks distinguishes the supernatural from the merely strange or unexplained? Or do we just get more revisionist physics?
The claim regarding the prior probability of miracles is obfuscatory nonsense. Either the guy doesn’t understand Bayesian arguments or is just muddying the waters to make what he wants to be true more probable. This is the problem with philosophical arguments. Whether the outcome is true depends upon the truth of the premises, so these people just keep fiddling with premises to find something with the appearance of truth because there really are no standards for discerning truth. So we have ridiculous arguments that “prove” the existence of their god and now that Bayseian reasoning has come along, they are trying to make arguments that look reasonable sound like they are on their side by making ridiculous claims.
Sure miracles have high prior probability. Just ignore the fact that not a single miracle has ever been showing to have happen. many claimed, many debunked, none proved. That automatically makes the prior <1%.
“Sure miracles have high prior probability. Just ignore the fact that not a single miracle has ever been showing to have happen. many claimed, many debunked, none proved. That automatically makes the prior <1%."
Yup. Apologists tend to love leaving facts out. The fact that there are so many debunked miracle claims is a strike against miracles. The evidence for any given miracle claim would have to be incredibly good, given that there is such a low prior. Feser might be aware that the evidence for the resurrection is not incredibly good, so that's (maybe) why he won't grant the very low prior.
I think it is a mistake to understand miracles in the christian sense as involving low or high probability. A miracle rather is just God acting in a way that suspends natural laws.
Yes, but what does that look like? How does divine, miraculous action look different than mundane action in its metaphysics?
If God causes everything to fall up for a second, then we were just wrong about physics a little bit. That is not surprising, and does not grant God a metaphysically distinct status.
I think that Feser’s original argument is mostly legitimate. Of course, as you say, miracles are still improbable- if they weren’t, they wouldn’t be nearly as “miraculous!” However, if one posits the belief in the classical theistic God- the omnipotent, omnibenevolent, and omniscient being who is pure act- then it only makes sense that this God would reveal himself in some way to the world. Thus, it makes sense that one of the three Abrahamic religions who worship this God, or at least other of the monotheistic religions, would be correct, no?
From there, one can base their faith on which religion they think is more likely, which would likely be the one with the greatest historical basis or theology. Hence, there is a need to discuss probability, but if you can already show that God exists, then I’d say the probability of something like the resurrection is already fairly high. Henceforth, faith can come into the picture there- not a blind faith, but faith based on prior reason.