\begin{align*} P( X > a + b | X > b ) & = \frac{P( X > a + b \cap X > b )}{P( X > b)}\\ & = \frac{P( X > a + b )}{P( X > b)}\\ & = \frac{(1-p)^{a+b}}{(1-p)^b}\\ & = (1-p)^a\\ & = P(X > a) \end{align*}