$\Large P(B/A)=\frac{P(A)+P(B)-P(A\cup B)}{P(A)}$
Also $P(A)+P(B)>1$
$\Rightarrow P(A)>1-P(B)$
$\Rightarrow P(A)>1-P(\bar{B})$
$\Rightarrow\Large\frac{P(\bar{B})}{P(A)}<1$
$P(B/A)=\Large\frac{P(A)}{P(A)}+\frac{P(B)-P(A\cup B)}{P(A)}$
$=\Large1+\frac{1-P(B')-P(A\cup B)}{P(A)}$
=$\Large 1-\frac{P(B')}{P(A)}+\frac{1-P(A\cup B)}{P(A)}$
$\Rightarrow\Large P(B/A)\leq 1-\frac{P(B')}{P(A)}$
The given statement is False.