Suppose we have a sphere centered at $(0, 0, 0)$, with the radius of $R_b$. We cut the sphere with the tangent plane centered at $(0, 0, R_a)$, where a dude is fixed on. (Here $0 < R_a < R_b$, always) Then we have spherical cap here.
From the dude, the minimum distance from him to any point will be $R_b - R_a$, as a vertical line. The maximum distance will be $\sqrt{{R_b}^2-{R_a}^2}$, as an end of horizontal line to sphere.
My question is, if we consider all the points on the spherical cap is available, how can we define the probability density function (PDF) of the distance from $(0, 0, R_a)$ to the spherical cap? I don't have any clue right now, so please help if there's any tips!