How did the Spanish word "éxito" come to mean "success"?

The word éxito in Spanish (and cognates in other iberian romance languages) has the meaning of success, but it is a cognate of English "exit".

According to Wiktionary, they all come from Latin "exitus", which is a participle of "exire", which literally means "to go out/outside, to exit, to leave".

Also on the Wiktionary page for this word is someone asking about this apparent semantic shift in Spanish, which got me wondering as well. Further googling only told me that it's not just Spanish but also Galician and Portuguese, possibly more.

Does anyone have information on how this shift developed? Or is the written evidence we have so poor that it might just as well have suddenly acquired the current meaning overnight as gradually over several generations and we wouldn't be able to tell?