Probability of dependent events and conditional probability formulas circling back to each other?

According to the multiplication rule, the probability of dependent events A and B happening is:

P ( A and B ) = P(A) times P ( B | A )

but how do we find P ( B | A ) ? We look at the conditional probability formula right?

But the conditional probability formula is

P ( A | B ) = P(A ∩ B) / P (B)

But then how do we find P(A ∩ B) ? We go to the multiplication rule?

Why does it create an endless loop of circular reasoning?