Step-by-step explanation:
De Leon eventually lost the power struggle and the governorship, tho he did get wealthy while being governor. Still, Ponce De Leon was out of a job.
But King Ferdinand was still curious about what else was in the neighborhood and De Leon was available. Besides, King Ferdinand figured that (a) De Leon should get rewarded somehow and (b) he could shaft Diego Columbus if De Leon did the exploring and got the credit.
The contract between De Leon and King Ferdinand specified that De Leon financed the expedition by himself, which he did. In exchange, De Leon became governor of anything he found, plus he got a big share of any profits in the form of gold, slaves, and other valuables. No Fountain of Youth.
And that’s why Juan Ponce De Leon found Florida and several islands: curiosity, greed, and a bit of revenge.