No secret is safe

Harry Potter and the Prisoner of Azkaban: Chapter 10

Harry has become quite the unintentional eavesdropper. You almost get the feeling that there's a man behind the curtain orchestrating things. But this isn't Oz.

The map is like a magical GPS with satellite imagery, like watching an episode of "NCIS: Los Angeles" or "Enemy Of The State." Harry uses this magicnology just to buy candy, but ends up gaining more knowledge of his parents, himself, Black, etc.

What will Harry and his cohorts do with this knowledge? Somehow some of it will help them catch Black. After the first two books, that it is what I'm expecting. If the Dementors couldn't dement him in prison and let him escape, then how will they catch him? Only Harry will catch or kill him.

The logical conclusion is that Harry will use the map to catch Black. But logical conclusions don't always happen in the world of magic. Logically, Harry should have died in the first book. But this wouldn't be much of a series if that had happened.

Here's a logical idea. Cast one of those Secret-Keeper spells so Black can't find Harry. That's what I would do.