# Can a posterior probability be >1?

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:
$P(a|x) = P(a\cap x) / P(x) \leq P(a) / P(x)$