The complement of P(B | A) is 1 - P(B | A). Is it also true that 1 - P(B | A) = P(B' | A), where B' means the complement of B?

Answer 1

1-P(B|A)
=1-P(B∩A)/P(A)
=( P(A)-P(B∩A) ) / P(A)
=P(A\B)/P(A)

P(B'|A)
=P(B'∩A)/P(A)
=P(A\B)/P(A)

So yes, they are equivalent.
=