Why would war with Athens a Sparta make Persia strong?

War between Athens and Sparta would potentially strengthen Persia by weakening both city-states, which had been significant rivals in the region. If they were engaged in prolonged conflict, Persia could exploit the situation to expand its influence over the Greek city-states or reassert control over previously lost territories. Additionally, a divided Greece would be less capable of resisting Persian ambitions, allowing Persia to re-establish itself as a dominant power in the Mediterranean. This strategy of encouraging and taking advantage of rivalries among its adversaries was a hallmark of Persian foreign policy.