Purpose of giving up a prisoner on the Passover Why did they give over a prisoner during the Passover? What was the reason for that
Like many judicial systems, the Roman legal system had provisions for pardoning of crime. It is likely the appointed time for pardon appeals coincided with the passover because that was the time many of the Jews in the region came to the city. In other words, it was politically expedient for the governing officials to grant a request before the largest audience of each the year.

(Not unlike how politicians today use "phtot-ops" at events with large public appeal, but then sign lesser received legislation on Fridays right after all the press goes home for the weekend...)