Homepage › Solution manuals › Joseph Blitzstein › Introduction to Probability › Exercise 2.18
P(B) = P(A ∩ B) + P(Ac ∩ B).
P(Ac ∩ B) = P(Ac)P(B|Ac) = 0, since P(Ac) = 1.
Thus, P(B) = P(A ∩ B) = P(B)P(A|B)⟹P(A|B) = 1.