Could you help me with conditional probability

Could you please explain to me how to do conditional probability

and how you would do this P(A|A'nB') the numbers in the venn diagram are in set A 0.25 in set B 0.3 and the intersection is 0.3 and the number in none of the sets ar 0.45

thankyou

P(A | A' ∩ B')
= P(A ∩ (A' ∩ B')) / P(A' ∩ B'), by definition of conditional probability
= P((A ∩ A') ∩ B') / P(A' ∩ B')
= P(Ø ∩ B') / P(A' ∩ B')
= P(Ø) / P(A' ∩ B')
= 0.

I hope this helps!