Cournot's principle states that a typical event (i.e., an event with probability very close to 1) occurs nearly certainly in a single trial of an experiment. This principle has been considered by various authors as the only connection between mathematical probability and the real world of experiments. To make the logical structure of the principle clearer, in this paper a reformulation of the principle is proposed. This reformulation is based on the following three elements: (1) The explicit definition of the empirical property of practical certainty, (2) the clear separation between probability measure and experiment, including the remark that typicality is a mathematical property defined by the probability measure while practical certainty is an empirical property defined by the experiment, and (3) the explicit formulation of the product rule for independent trials. The novel formulation then states that a probability measure P "governs" an experiment E if the events that are typical according to P^n are practically certain according to E^n for all n >= 1, where P^n is the n-fold product of P and E^n is the experiment whose trials are composed of n trials of E. The novel formulation highlights the possible existence of two ambiguities in the principle, namely: (i) that different probability measures govern the same experiment and (ii) that the same probability measure governs different experiments. In this paper the first ambiguity is rigorously disproved, while the second is disproved provided that a suitable property characterizing the empirical equivalence of experiments is assumed.