Using the definition of conditional probability, we have
[tex]\mathbb P(E\mid F)=\dfrac{\mathbb P(E\cap F)}{\mathbb P(F)}=\dfrac{\mathbb P(F\mid E)\cdot\mathbb P(E)}{\mathbb P(F)}[/tex]
so the probability we want is
[tex]\dfrac{\dfrac58\cdot\dfrac23}{\dfrac34}=\dfrac59[/tex]
