Rational agents should integrate probabilities in their predictions about uncertain future events. However, whether humans can do this, and if so, how this ability originates, are controversial issues. Here, we show that 12-month-olds have rational expectations about the future based on estimations of event possibilities, without the need of sampling past experiences. We also show that such natural expectations influence preschoolers’ reaction times, while frequencies modify motor responses, but not overt judgments, only after 4 years of age. Our results suggest that at the onset of human decision processes the mind contains an intuition of elementary probability that cannot be reduced to the encountered frequency of events or elementary heuristics.