  We construct a probabilistic model for the number of divisors of a random
uniform integer that converges in the mod-Poisson sense to the same limiting
function as its original counterpart, the one arising in the Sathe-Selberg
theorem. This construction involves a conditioning and gives an alternative
perspective to the usual paradigm of "hybrid product" models developed by
Gonek, Hughes and Keating in the case of the Riemann Zeta function.
