Iterated dominance is perhaps the most basic principle in game theory. The epistemic foundation of this principle is based on the assumption that all players are rational. The main contribution of this paper is to characterize the algorithm of iterated admissibility in Probabilistic Epistemic Game Logic (PEGL). Firstly, on the basis of Probabilistic Epistemic Logic we set up a logic PEGL. Secondly, by redefining a concept of rationality, we show that the common knowledge of the rationality characterizes the algorithm of Iterated Admissibility, that is, we provide an epistemic foundation for the solutions or equilibria which are found by the algorithm of Iterated Admissibility(IA). Next, we provide a different characterization of IA using public announcements of the rationality in dynamic logic. The results we obtain can be seen as giving a dynamic epistemic foundation for the algorithm of Iterated Admissibility.