# How to find a conditional probability density function

How to find the conditional probability density function $P(X>Y\mid \max(X,Y)>T)$. $X,Y$ are independent identical exponential random variables. $T$ is a constant. Is it possible to find at least the value for a given $T$?

If $X$ and $Y$ are iid exponentially distributed random variables, then by symmetry $\Pr(X\gt Y|\max(X,Y)\gt T)=1/2$.