  It is conventional to calculate the probability of microlensing for a
cosmologically distant source based on the Press-Gunn approximation that the
lensing objects are uniformly and randomly distributed in the intervening space
with a constant comoving density. Here we investigate more realistic
cosmological microlensing statistics by considering the strong spatial
clustering of likely lensing objects with each other in galaxies and their
association with the clumps of dark matter that make up the massive halos of
galaxies. The distribution of microlensing optical depth (kappa) along randomly
chosen sight lines is calculated as is the conditional distribution of kappa
along sight lines near one which is strongly microlensed. Our overall result is
that the Press-Gunn approximation is a useful order-of-magnitude approximation
if the massive halos of galaxies are made of dark compact objects but that it
fails badly and can be qualitatively misleading in the more likely case in
which only the ordinary stellar populations of galaxies are the dominant source
of cosmological microlensing events. In particular, we find that microlensing
by stars is limited to of order 1 percent of high redshift sources at any one
time. Furthermore, even though only a small fraction of high redshift sources
are multiply-imaged (by galaxies), it is these sources that are most likely to
be microlensed by stars. Consequently, microlensing by stars is usually
observed at kappa's near 1 where the simple isolated point mass lens
approximation is not appropriate. However, if CDM halos are composed of
condensed objects, then more than 10 percent of high redshift sources are
microlensed at any given time. The vast majority of these sources are not
multiply-imaged, and have kappa's smaller than 0.01.
