  We address the problem of the apparently very small magnitude of CP violation
in the standard model, measured by the Jarlskog invariant J. In order to make
statements about probabilities for certain values of J, we seek to find a
natural measure on the space of Kobayashi-Maskawa matrices, the double quotient
U(1)^2\SU(3)/U(1)^2. We review several possible, geometrically motivated
choices of the measure, and compute expectation values for powers of J for
these measures. We find that different choices of the measure generically make
the observed magnitude of CP violation appear finely tuned. Since the quark
masses and the mixing angles are determined by the same set of Yukawa
couplings, we then do a second calculation in which we take the known quark
mass hierarchy into account. We construct the simplest measure on the space of
3 x 3 Hermitian matrices which reproduces this known hierarchy. Calculating
expectation values for powers of J in this second approach, we find that values
of J close to the observed value are now rather likely, and there does not seem
to be any fine tuning. Our results suggest that the choice of Kobayashi-Maskawa
angles is closely linked to the observed mass hierarchy. We close by discussing
the corresponding case of neutrinos.
