The first (and bigger) problem is you are committing an ontological error (probability distributions are not about causality but about uncertainty. It doesn’t matter if you are B or F about it).
I don’t know what you mean by this. Probability distributions can be about whatever you want — it makes perfect sense to speak of “the probability that the cause of X is Y, given some evidence”.
I don’t know what you mean by this. Probability distributions can be about whatever you want — it makes perfect sense to speak of “the probability that the cause of X is Y, given some evidence”.