Bayesian probability theory distinguishes between prior and posterity probability. From what I've read, prior probability is based on our background knowledge regarding what's possible or likely in general, while posterior probability takes into account specific information about the event under consideration. The way it's divvied up, an event may have low prior probability, but that initial presumption can sometimes be overcome by countervailing evidence.
As a rule, I just don't find this a helpful framework. Let's take two illustrations:
Consider a parking lot at a shopping mall or parking garage at an airport. Say there are a thousand cars. One of them is mine. I'm walking back to the parking lot or parking garage.
You could say the prior probability of me picking out any car in particular is one in a thousand. As a matter of pure math, that's true.
But it's a rather ridiculous way to cast the issue. Unless I see an irresistibly appealing sports car that I decide to hot-wire on the spur of the moment, it's 100% certain that I will drive my car home, and 100% certain that I won't drive any of the other 999 cars home.
So why would we even set up the calculations as if there's a heavy presumption against my driving my own car home, a presumption which–fortunately–can be overcome by additional information? Why frame the issue in such an abstract way that that's a low prior probability of me driving a car with that particular license plate? The mathematical odds just aren't relevant. I'm not picking a car at random.
Why divvy it up as if we have to begin in a state of relative ignorance, when in fact we have all the information? Why set it up as a balancing act?
Let's take another example: what are the odds that lightning will strike any particular tree? Well, we could start by comparing the number of lightning strikes during a given timespan to the number of trees in a given radius. And from that standpoint, the odds are remote that it will strike any particular tree.
Suppose, though, I go for a daily walk along a trail. I always pass by the same stately tree. Today I walk past that tree. Then I'm overtaken by a thunderstorm. I see a lightning strike behind me on the trail, and I hear something explode. But I don't see what was hit.
As I walk back, I see the familiar tree split in two, with scorch marks. I conclude that it was struck by lightning. Although it's antecedently improbable that lightning would single out this tree, the abstract chances of that happening have no bearing on my well-founded belief that this tree was struck by lightning. Why would I even take prior probability into account?
I'm not saying this is never germane. It may be antecedently improbable that the brakes will fail on a recently serviced, high-end sports car, causing the driver to die. The very implausibility of mechanical failure may make the homicide detective suspicious, so he sniffs around until he finds out the wife of the decedent was having an affair with dashing automechanic to serviced the car a day before. The circumstantial evidence is very incriminating. Means, motive, and opportunity.
My problem, though, is when the case for miracles is always shoehorned into a framework where miracles are assigned a very low prior probability. A standing presumption against miracles. It's then up to the Christian apologist to surmount the daunting odds. It's like winning when the deck is stacked against you. Impressive if you can, but why should we frame the issue that way in the first place? It's gratuitously prejudicial.