The Persian war still set the conditions for the peloponnesian war because

Because Athens and Sparta, both powerful Greek city-states, had fought as allies in the Greco-Persian Wars between 499 and 449 B. C. In the wake of the Persian retreat, however, Athens grew more powerful and tensions rose, escalating into nearly three decades of war. Sparta emerged victorious, while the constant fighting left Athens bankrupt, exhausted and demoralized. Neither city-state regained the military strength they once had