Bounding probability of picking point from $l^p$ ball

Question

Consider picking $x$ randomly and uniformly from the $l^p$ ball with radius $R$, $B_p^d(R)$. If $0\le \gamma \lt 1$, how can I conclude following? $$ P(\| x\|_p \le \gamma R) = \frac{\operatorname{Vol}(B_p^d(\gamma R))}{\operatorname{Vol}(B_p^d(R))} $$