Density in solid angle $\Omega$ convert to spherical angles $\theta$ and $\phi$

Question

I was given a probability density $$ \frac{dP}{d\Omega} $$ where $\Omega$ is the solid angle such that $$ d\Omega = \sin \theta \ d\theta \ d\phi $$ and $\theta$ and $\phi$ the sperical coordinates angles. To obtain the probability we calculate the integral $$ P = \int \frac{dP}{d\Omega} \ d\Omega = \int \frac{dP}{d\Omega} \ \sin \theta \ d\theta \ d\phi .$$ Is it correct, then, that the probability density on the spherical angles $\theta$ and $\phi$ is $$ \frac{dP}{d\theta \ d\phi} = \frac{dP}{d\Omega} \sin \theta \ ?$$