  We construct a natural measure on the space of CKM matrices in the standard
model, assuming the fermion mass matrices are randomly selected from a
distribution which fits the observed quark mass hierarchy. This measure allows
us to assess the likelihood of Jarlskog's CP violation parameter J taking its
observed value J $\approx$ 3 x 10^{-5}. While well below the mathematically
allowed maximum, we find that this value is in fact typical, once the observed
quark masses are assumed.
