If [tex]A^C[/tex] has occurred, then [tex]A[/tex] cannot occur, so the probability is 0.
This follow directly from the definition of conditional probability:
[tex]P(A\mid A^C)=\dfrac{P(A\cap A^C)}{P(A^C)}[/tex]
but [tex]A[/tex] and [tex]A^C[/tex] are disjoint, so the probability of their intersection is 0.
