\begin{align*} P( X > a + b | X > b ) & = P( X > a + b \cap X > b ) \ P( X > b)\\ & = P( X > a + b ) / P( X > b)\\ & = e^{-(a+b)/ \mu} / e^{-b / \mu}\\ & = e^{-a/ \mu}\\ & = P(X > a) \end{align*}