The problem of what to expect from the black box?

I'd think about it like this: suppose that I hand you a box with a slot in it. What do you expect to happen if you put a quarter into the slot?

To answer this we engage our big amount of human knowledge about boxes and people who hand them to you. It's very likely that nothing at all will happen, but I've also seen plenty of boxes that also emit sound, or gumballs, or temporary tattoos, or sometimes more quarters. But suppose that I have previously handed you a box that emits more quarters sometimes when you put quarters in. Then maybe you raise the probability that it also emits quarters, et cetera.

Now, within this model you have a probability of some payoff, but only if it's one of the reward-emitting boxes, and it also has some probability of emitting sound etc. What you call a "meta-probability" is actually the probability of some sub-model being verified or confirmed. Suppose I put in one quarter in and two quarters come out - now you've drastically cut down the models that can describe the box. This is "updating the meta-probability."