This talk considers nonstationary two-person zero-sum stochastic games under a probability criterion. Under a mild condition, we establish a comparison theorem, and derive a sequence of the Shapley equations for the probability criterion. Using the comparison theorem, we prove the existences of the value of the game and a Nash equilibrium. Moreover, we provide a value iteration-type algorithm for computing the value of the game and epsilon-Nash equilibria. Finally, an inventory-production example is presented to illustrate the applications of our results.