The problem of probabilistic caching in a network with multiple edge nodes and user nodes is studied. Files with different lengths, caches with different sizes, and spatial coupling through overlapping service areas are considered. The connection between caching probabilities and strategy-mixing probabilities in a mixed strategy is characterized. It is found that a given set of caching probabilities for an edge node can correspond to more than one mixed strategies. Through this characterization, caching probabilities can be decomposed into pure caching strategies and corresponding strategy-mixing probabilities. Moreover, the best-response caching strategy of an EN is studied and obtained based on the spatial-coupling discounted file preference level. The impact of information availability and request scenario on the best-response strategy is analyzed. Numeric examples demonstrate the best-response strategy and the decomposition of the caching probabilities into pure strategies and strategy-mixing probabilities.