When multiple communication systems share a particular frequency band, each system operates subject to interference generated by the others. In this environment, an accurate assessment of the effects of interference is very important. Given the complexity of the problem, interference calculations is usually done considering a number of worst case conditions and simplifying assumptions. They include, for example, the hypothesis that the degradation due to rain is only present in the victim link and do not affect any of the interfering links, the hypothesis that earth stations involved are located at the most unfavorable sites (in terms of interference) within their service areas, and the use of a reference diagram for radiation antenna patterns. These hypotheses imply a conservative calculation of interference in which obtained interference levels are higher than their actual levels. In this work, as an alternative to the assumption that the earth stations are located at the most unfavorable sites of their service areas, a probabilistic model is used. In the proposed model the geographic locations of the ground stations are characterized by random vectors. As a consequence, the resulting carrier interference ratio is also a random variable and its statistical behavior is also evaluated in this work. Numerical results are obtained for particular situations involving multiple multi-beam satellite communication networks operating in the Ka band. The results are compared to those obtained under the assumption that the Earth stations are located at the most unfavorable sites of their service areas. Finally, the joint effect of modeling both, the ground station locations and their antena sidelobe gains, as random quantities was evaluated.