  In theories in which the cosmological constant Lambda takes a variety of
values in different ``subuniverses,'' the probability distribution of its
observed values is conditioned by the requirement that there must be someone to
measure it. This probability is proportional to the fraction of matter which is
destined to condense out of the background into mass concentrations large
enough to form observers. We calculate this ``collapsed fraction'' by a simple,
pressure-free, spherically symmetric, nonlinear model for the growth of density
fluctuations in a flat universe with arbitrary value of the cosmological
constant, applied in a statistical way to the observed spectrum of density
fluctuations at recombination. From this, the probability distribution for the
vacuum energy density rho_V=Lambda/8pi G for Gaussian random density
fluctuations is derived analytically. It is shown that the results depend on
only one quantity, sigma^3 RHO, where sigma^2 and RHO are the variance and mean
value of the fluctuating matter density field at recombination, respectively.
To calculate sigma, we adopt the flat CDM model with nonzero cosmological
constant and fix the amplitude and shape of the primordial power spectrum in
accordance with data on cosmic microwave background anisotropy from the COBE
satellite DMR experiment. A comparison of the results of this calculation of
the likely values of rho_V with present observational bounds on the
cosmological constant indicates that the small, positive value of rho_V (up to
3 times greater than the present cosmic mass density) suggested recently by
several lines of evidence is a reasonably likely value to observe, even if all
values of rho_V are equally likely a priori.
