Given $\displaystyle f(y)= 2y^{-3}$ , if $\displaystyle y\geq\\ 1$ and 0 otherwise, the probability

$\displaystyle P(2\leq\\Y\leq\\4|Y\geq\\3)=?$

I was thinking, $\displaystyle P(2\leq\\Y\leq\\4|Y\geq\\3)=

\frac{P(2\leq\\Y\leq\\4\cap\\Y\geq\\3)}{P(Y\geq\\3 )}

=\frac{P(2\leq\\Y\leq\\4}{P(Y\geq\\3)}$.

I drew out the cdf and shaded the regions in question, but I am not sure how to treat the numerator.

Thanks