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Recent research shows that preverbal infants can reason about single-case probabilities without relying on observed frequencies, adapting their predictions to relevant dynamic parameters of the situation (Téglás, Vul, Girotto, Gonzalez, Tenenbaum & Bonatti, [Téglás, E., 2011]; Téglás, Girotto, Gonzalez & Bonatti, [Téglás, E., 2007]). Here we show that intuitions of probabilities may derive from the ability to represent a limited number of possibilities. After watching a scene containing moving objects of two ensembles, 12-month-olds looked longer at an unlikely than at a likely single-case outcome when the objects were within the parallel individuation range. However, they did not do so when the scene contained the same ratio between ensembles but a larger number of objects. At the same time, they could form rational expectations about single-case outcomes in scenes containing the same large number of objects when they could exploit subtle physical parameters induced by the objects' movements and their spatial configuration. Our findings demonstrate that at early stages of development the mental representations involved in probability estimations of future individual situations are powerful and sophisticated, but at the same time they depend on infants' overall cognitive architecture, being constrained by the numerical representations spontaneously induced by the situations.