Triangles $XYZ$ and $PQR$ are similar, with angle $X$ corresponding to angle $P$ and angles $Z$ and $R$ being right angles. The ratio of the length of $\overline{XY}$ to the length of $\overline{PQ}$ is $3:1$. If $\cos X=\frac{7}{25}$, what is the value of $\sin P$?