I'm guessing "a^b" is meant to denote the intersection, or possibly [tex]A^B[/tex] which could be the complement of [tex]B[/tex] in [tex]A[/tex]. I'll stick with the first assumption. I'll also read "a/b" as [tex]A\mid B[/tex], the event of [tex]A[/tex] being conditioned on [tex]B[/tex], though this also is ambiguous and could refer to the complement of B in A.
By definition of conditional probability,
[tex]\mathbb P(A\mid B)=\dfrac{\mathbb P(A\cap B)}{\mathbb P(B)}=\dfrac{\frac34}{\frac45}=\dfrac{15}{16}[/tex]
