  We consider the Cauchy problem for the massive Dirac equation in the
non-extreme Kerr-Newman geometry outside the event horizon. We derive an
integral representation for the Dirac propagator involving the solutions of the
ODEs which arise in Chandrasekhar's separation of variables. It is proved that
for initial data in L^\infty_loc near the event horizon with L^2 decay at
infinity, the probability of the Dirac particle to be in any compact region of
space tends to zero as t goes to infinity. This means that the Dirac particle
must either disappear in the black hole or escape to infinity.
