Suppose I get a piece of evidence apparently relevant to a proposition p that can't be handled using the standard Bayesian probabilistic apparatus. For instance, maybe I am trying to figure out how close a dart landed to the center of the target, and I learn that, mirabilis, the dart's landing point had rational numbers as coordinates. That's a case where the likelihoods of the evidence on all the relevant hypotheses are zero and there is no good limiting procedure to get around that. Or maybe I am trying to figure out how old Jones is, and I am told that Jones' age in years happens to be equal to a number that an angel yesterday picked out from among all natural numbers by a procedure that has no biases in favor of any numbers. That's a case where there are no meaningful likelihoods at all, since countable fair lotteries cannot be handled by the probability calculus. Or perhaps I am wondering whether some large number is prime, and I am told that infinitely many people in the multiverse think it is and infinitely many think it's not.
In some cases, the evidence should infect my credences in such a way that I no longer have a probability assigned to p. In other cases, I should just ignore the evidence. How to judge what should be done when? My intuitions say that I can just ignore what the infinitely many people in the multiverse think. But I don't know what to make of the other two pieces of evidence. I have a weak inclination to ignore the rational-number-coordinates fact. But the fact about Jones' age happening to match up with the infinite lottery result, that I don't think should be ignored. Maybe I should no longer have credences about Jones' age?
Can anything in general be said? Maybe, but I don't know how to do it.