Preference for a Vanishingly Small Cosmological Constant in Supersymmetric Vacua in a Type IIB String Theory Model

We study the probability distribution P(\Lambda) of the cosmological constant \Lambda in a specific set of KKLT type models of supersymmetric IIB vacua. We show that, as we sweep through the quantized flux values in this flux compactification, P(\Lambda) behaves divergent at \Lambda =0^- and the median magnitude of \Lambda drops exponentially as the number of complex structure moduli h^{2,1} increases. Also, owing to the hierarchical and approximate no-scale structure, the probability of having a positive Hessian (mass squared matrix) approaches unity as h^{2,1} increases.