Diagnostic computations of two main characteristics of grid-scale forcing of ascending motions in the atmosphere, that is, of frontal parameter F and level of neutral buoyancy (convection level) LNB are presented as based on the objective analysis and numerical forecasting data. The computed diagnostics are compared with the observed precipitation amounts at the stations. It is found that convective instability in the deep layers (of large vertical thickness) mostly results in heavy precipitation, while shallow instability (of small vertical thickness), mostly in light precipitation. It manifests itself in monotonous growth of frequency of moderate, heavy, and very heavy precipitation with growing F and LNB; on the contrary, the light precipitation frequency is maximum under LNB = 2-3 km. At the intense fronts, convective instability is found to be forced in about a half of the case numbers; in winter and summer, instability is forced mainly in the shallow and deep layers, respectively. Frequency distributions of the precipitation rate ranges as dependent on F and LNB are presented as computed from the 10-year data series in the European territory of the former USSR: they are interpreted as the area-and time-averaged spectra of precipitation rate probabilities. As more practical and descriptive, the precipitation probability spectra are introduced as dependent on the predicted precipitation amount in the gridsquare. By the example of semi-Lagrangian model of Hydrometeorological Center of Russia and the NCEP global model (the United States), it is shown that generally the predicted precipitation range is not the most probable: as a rule, the most probable is a lower range of precipitation rate. The presented results can be considered as a demonstration of a possible way to develop a substantiated and reliable method to forecast the probability distribution of the precipitation rate ranges based on the numerical categorical forecast.