Valid circumstances where P(A) = P(A|B)⋅P(B)

Question

Normally we would say that:

$$\ P(A\cap B) = P(A|B)⋅P(B) = P(B|A)⋅P(A) $$

but I am wondering if there are any valid circumstances where this would hold true:

$$\ P(A) = P(A|B)⋅P(B) $$

I was thinking that if B was the only thing that caused A, that this would be true. I swear I saw this in a textbook somewhere but now I can't find it.

Answer 1

Just to formalize your answer in the comments a little better:

If $A\subseteq B$ then $A\cap B$=$A$ and therefore $\text{Pr}(A\cap B)=\text{Pr}(A)$.