Are there any branches of mathematics where causality is incorporated? For example, in Bayesian probability:
$$ \ P(B|A) = \dfrac{P(A ∩ B)}{P(A)} \ $$
likewise:
$$ \ P(B|A) = \dfrac{P(A | B)P(B)}{P(A)} \ $$
there doesn't seem to be a notion of time or causality since A could happen before B or vice versa.
Is there a way to determine that B is a necessary but not sufficient event for A to happen, for example? For example, the probability that B happens given A is zero B happens before A, but some other value if A happens first?