We present a search for associated production of the standard model Higgs boson and a Z boson where the Z boson decays to two leptons and the Higgs decays to a pair of b quarks in pp collisions at the Fermilab Tevatron. We use event probabilities based on standard model matrix elements to construct a likelihood function of the Higgs content of the data sample. In a CDF data sample corresponding to an integrated luminosity of 2.7  fb−1 we see no evidence of a Higgs boson with a mass between 100  GeV/c2 and 150  GeV/c2. We set 95% confidence level upper limits on the cross section for ZH production as a function of the Higgs boson mass mH; the limit is 8.2 times the standard model prediction at mH=115  GeV/c2.