Here's a resource in technical language about
Bayes Theorem. In reality the math is pretty trivial, and in most poker contexts you can just think of it as common sense.
In the context of poker, we use Bayes Theorem mostly to compute the relative likelihood of certain events, given some information. For instance, in the hand loosely in question, a 9 completed, there was another 9 dead, and I had split kings. So given those cards were out, IF we assume the raiser with the 9 had either kings, aces or rolled nines, we use Bayesian analysis
to determine the relative likelihood of those hands. Since there are only 2 nines unaccounted for, and two kings unaccounted for, there is only 1 way of having each of those hands. Meanwhile there are 6 ways of having aces buried. So there's a 6/8 chance he has aces, a 1/8 chance of kings and 1/8 chance of rolled. (These are relative probabilities given the cards we see, rather than the absolute probabilites of something like 1/(420*13) chance of being dealt rolled nines in general, for instance.)
So what I want to say, is given the cards out and the fact that the nine raised, but NOT assuming the player is good, what are the relative likelihoods of a) the player being any good b) the player holding various hands.
So as we just learned, a good player could raise 8 hands there. Let's say a bad player would raise any pair, but not other hands, for the sake of this example. Given the cards that are out that means something like about 70 hands. Now if P is the probability that an unknown player is good in general, and 1-P is the probability that an unknown player is bad, we can figure out from those probabilities PLUS the fact that the player raised with a 9 up what the conditional probability that this player is good is, like this:
8*P/(8*P + 70*(1-P))
I think I did that right.
So what I'm really asking for is the overall population ratio of "good" to "bad" players, approximately, and also what hands I can expect a "bad" player to raise with, on average. This is clearly going to be pretty unscientific, part of my point is simply that I shouldn't guess this player is reasonable right off the bat. But I'd also like to get some subjective guesses about all this from players who play in that game more often than I do.