In Bayes’ formula:
can the posterior probability P(x|a) exceed 1?
I think it is possible if for example, assuming that 0<P(a)<1, and P(a)<P(x)<1, and P(a)/P(x)<P(a|x)<1. But I'm not sure about this, because what would it mean for a probability to be greater than one?
The assumed conditions do not hold- it can never be true that P(a)/P(x)<P(a|x) by the definition of conditional probability: