Distribution for the Ratio of Two Uniform Deviates

Weird: the distribution for the ratio of two uniform deviates is constant for ratios smaller than 1, and falls like r^2 for larger ratios. p(r) = 1/2 if r < 1, and 1/(2r^2) if r >= 1 when r = a/b, where a,b ~ U(0, A). What's up with that?