Various meteorological studies require probabilistic modeling such as the flood, drought, and wet and dry spell occurrences. The most commonly employed approaches are based on the binomial probability distribution function (pdf), which is valid for homogeneous temporal and spatial probabilities. However, in practice, heterogeneous probabilities are very common, and in this case, the classical binomial pdf cannot be employed. This paper presents a rigorous probabilistic methodology for heterogeneous probabilities by considerations from the random field concept. The general form of the binomial pdf is derived and it is shown that for homogeneous probabilities it yields the classical binomial pdf exactly. The necessary analytical formulations are derived with the assumption that the meteorological occurrences at a set of sites or time periods (day, month, and year) are independent from each other. The probability statements derived in this paper are helpful in predicting the regional and temporal probable potential future meteorological occurrences. The application of the proposed methodology is presented for annual precipitation occurrences at six meteorology stations around Istanbul, Turkey.