  We have calculated the probability that the clustering of arrival directions
of ultra-high energy cosmic rays (UHECRs) is consistent with a finite number of
uniformly distributed proton sources. The case of a continuous source
distribution is reached only for an unrealisticly high source density, $n_s\gg
10^{-2}/Mpc^3$. Even for densities as large as $n_s=10^{-3}/Mpc^3$, less than
half of the observed cluster are on average by chance. For the best-fit value
$n_s=(1-3)\times 10^{-5}/Mpc^3$ derived from the AGASA data, the probability
that at least one observed cluster is from a true point source is larger than
99.97%, while on average almost all observed clusters are true. The best-fit
value found is comparable to the density of AGNs and consistent with the recent
HiRes stereo data. In this scenario, the Pierre Auger Observatory will not only
establish the clustering of UHECRs but also determine the density of UHECR
sources within a factor of a few after one year of data taking.
