We present a method developed at D0 for extracting information from data through a direct calculation of a probability for each event. This probability, which is a function of any parameter of interest, is calculated by convoluting the differential cross section with the resolution and acceptance of the detector. The method is used to re-measure the mass of the top quark and to extract the fraction of longitudinal W bosons in the lepton + jets ttbar sample previously collected by the D0 experiment during Run I of the Fermilab Tevatron. The new method yields a top mass of Mtop=180.1+-3.6 (stat)+- 4.0 (syst) GeV/c2, which corresponds to a significant reduction in the uncertainty on Mtop. Assuming Standard Model coupling in the tbW vertex, we extract for the first time at D0 the longitudinal fraction F0=0.56+-0.31 (stat+Mtop)+- 0.04 (syst).