I'm posting this here because I want to see if my reasoning is incorrect.
Generally, when people talk about the problem of evil, the underlying problem is actually one of indifference. Given that God exists, he doesn't seem to care some (most) of the time bad things happen, and seems to sometimes reward bad people with good fortune. This makes sense, of course, if there indeed was no god, but we have thousands of years of theodicy that argues that an all powerful, all knowing god exists despite the problem of indifference.
So, I attempted to formulate the problem of indifference in terms of probability - the probability of an all powerful god creating the universe (H) verses the probability of naturalism (~H) - to see which one was more likely. E would be the state of the current universe which seems to have both "good" and "evil" in it. I had no idea how to determine the probability of P(E | H), but if the 2,500+ years of theodicy explaining the problem of indifference was in fact correct, then to be fair to theism I might grant that P(E | H) = .99. However, this seems to not be correct; I did know that P(E | H) + P(~E | H) = 1.00 so this would mean that the all powerful god of traditional theism wouldn't make sense if our universe were indeed ~E instead of E given that P(E | H) = .99.
~E would be any other ratio of good::evil that we can imagine outside of the current state of affairs, or at least that's my reasoning. This means that if the universe were all good and zero evil, or all evil and zero good, granting that P(~E | H) = .01 doesn't seem like something traditional theism would accept. If we woke up tomorrow, and there was absolutely no evil in the world, and that was how the world always was, would traditional theism have no theodicies that explained why this world was evidence for their god(s)? That doesn't seem likely. Similarly, but less so, for a world that was overwhelmingly evil with very little good.
So it seems that E and ~E can be broken up into these three scenarios. E1 being our current world, E2 being a world of all good an no evil, and E3 being a world of all evil and no good. Then we have P(E1 | H) + P(E2 | H) + P(E3 | H) = 1.00. This would also apply to naturalism, but it seems as though a world of all good/evil and no evil/good wouldn't make sense under naturalism which predicts a fundamentally uncaring universe; P(E | ~H) = .99 and P(~E | ~H) would make sense to be the remainder. If this is the case, then the likelihood ratio favors naturalism. P(E1 | H) / P(E1 | ~H) is less than 1 since traditional theism doesn't seem to be restricting anticipation on what type of world(s) it can explain while naturalism does.
But then I thought that this applies to more situations beyond just the problem of evil/indifference. If an all powerful all knowing god can explain any and every sort of evidence we can imagine, and if there are 100 different types of evidence in a given class of evidence, then this god's explanatory power gets stretched across all 100 types of evidence, with any other hypothesis that restricts the type of evidence it can explain being favored over the god hypothesis. For something like the fine tuning argument for god, since there are infinite combinations of physical constants that an all powerful, all knowing god could create, this stretches the god hypothesis out among an infinite number of possible evidences, effectively favoring any alternative hypothesis by infinite decibles via the likelihood ratio. Meaning that something like the fine tuning argument is ironically an argument against H.
And if this is the case, then an infinitely powerful, infinitely knowing god is infinitely less likely than any other hypothesis that restricts itself. Thoughts? Is my reasoning off somewhere? Is the the ultimate penalty for not restricting anticipation?
There is an argument in the vicinity of yours that I think is interesting. One popular theodicy is skeptical theism, the claim that we have basically no access to god's reasons for action, so we should not make claims like "God would probably have created a universe with less evil."
A consequence of skeptical theism seems to be that the distribution over possible world states, given the hypothesis that god created the world, should be close to maximum entropy. This means no observation of the world state could count as much evidence for the hypothesis.
This seems like the point you're flirting with here, and I think it's a good one, but unfortunately it is obscured by your bad math.
"unfortunately it is obscured by your bad math."
That's what I'm hoping someone will explain