If the occurrence of A will not affect the occurrence of B, it is said that A and B are independent of each other.

In conditional probability, when P(B|A)=P(B), it means that the occurrence of A will not affect the occurrence of B, so there are the following judgment methods.

P(B|A)=P(AB)÷P(A)=P(B)

That is, p (ab) = p (a) p (b)

A common example can be: tossing the heads of two even coins A, B and A will not affect the probability of the head of B! Thus, A = A appears in front, and B = B appears in front. These two events are independent.

But in general, it is more accurate to judge with P (AB) = P (A) P (B)!

And what you said AB = φ refers to the case that two events A and B are incompatible, that is, mutually exclusive!

You can ask questions if you don't understand. If it helps, please choose the satisfactory answer!