I'm taking an intro to statistics class and currently we are covering conditional probability. The chapter explained what it is quite well, but it didn't explain how the formula for it was derived, i.e it didn't explain explain how

$P(A|B) = \frac{P(A \cap B)}{P(B)}$

was derived.

I would greatly appreciate if someone could show the reasoning as well as derivation of this formula.

I'm taking an intro to statistics class and currently we are covering conditional probability. The chapter explained what it is quite well, but it didn't explain how the formula for it was derived, i.e it didn't explain explain how

$P(A \mid B) = \frac{P(A \cap B)}{P(B)}$

was derived.

I would greatly appreciate if someone could show the reasoning as well as derivation of this formula.