Let $Z_{t}= W_{t}-tW_{1}$ and $Y_{1}=\sup_{0\leq t\leq 1}Z_{t}$, $(W_t, t \geq 0)$ standard Brownian motion
Find the law of $Y_{1}$
I know that $\textbf{P}(\sup_{0\leq t\leq 1}W_{t}\geq x , W_{1}\leq y) = \textbf{P}(W_{1}\geq 2x-y)$ $\forall x\geq y$,$\forall x\geq 0$
Now I want to find $\textbf{P}(Y_{1}\geq x)$
Some help would be appreciated