I'm stuck on an exercise, which goes as follows: Let $ X $ be an exponentially distributed random variable. Show that \begin{equation} P(X\leq s+t\mid X>s)=P(X\leq t) \end{equation} for all $ s,t\geq0 $.
I know that $ P(X\leq s+t|X>s)=\frac{P((X\leq s+t)\cap(X>s))}{P(X>s)} $. But I don't know how to further rearrange the numerator.
I have seen proofs for a similar equation, but never for this one. Can someone help me or give a hint, how I could show this?