This paper presents a mathematical model for the prediction of the probabilities of reverse power flow exceeding predefined critical thresholds at feed-in points of a distribution network. The parametric prediction model is based on hourly forecasts of global horizontal irradiation and uses copulas, a tool for modeling the joint probability distribution of two or more strongly correlated random variables with non-Gaussian (marginal) distributions. The model is used for determining the joint distribution of forecasts of global horizontal irradiation and measured solar power supply at given feed-in points, where respective sample datasets were provided by Deutscher Wetterdienst and the N-ERGIE Netz GmbH. It is shown that the fitted model replicates important characteristics of the data such as the corresponding marginal densities. The validation results highlight strong performance of the proposed model. The copula-based model enables to predict the distribution of solar power supply conditioned on the forecasts of global horizontal irradiation, thus anticipating great fluctuations in the distribution network.