Great man, Dumbeldore... He gives people second chances, see...
We see this also with Snape's story at the end of Deathly Hallows.
Pesach Sheni is a minor holiday, celebrated today (May 19, 2008), where the Torah teaches us the principle of second chances. 3300 years ago, when the first Passover holiday was celebrated a year after the Exodous from Egypt, some of the Jews had missed celebrating the holiday because they weren't in a state of purity to be able to bring the Passover offering. G-d told Moses that they could do so a month later.
While we don't truly celebrate Pesach Sheni in any way nowadays, since we can't bring the Passover offering at all, we still remember Pesach Sheni as the day that G-d taught us about second chances. If someone has the desire to do the right thing, there will always be a second chance for them to do so.