How did Dumbledore find out that the Deathly Hallows are real objects?

[Nicolas Flamel]

I'm trying to figure out how Dumbledore learned that all Deathly Hallows were real objects.

In Deathly Hallows we see rationalist Hermione arguing with Xenophilius ("lover of the strange") Lovegood.

Ironically, Xenophilius is right about the existence of these objects.

The Elder Wand is the most visible object, one can follow its trace through history. Dumbledore and Grindelwald obviously know the story of the three brothers. They know the stories about the wand that is called the Elder Wand.

But why would they think that the other two Hallows are also real? Perhaps they didn't think so and only later Dumbledore learned that they are in fact real.

James Potter gives Dumbledore the invisibility cloak. Perhaps his 'curiosity' was that this object confirmed the existence of the second Hallow? I can imagine that this can be quite overwhelming for Dumbledore for a moment.

And the same of the resurrection stone when he discovers in the house of the Gaunts, the confirmation that all Hallows are real.

[patricio]

I think your theory is accurate, and there is no "official" confirmation of when Dumbledore realized the Deathly Hallows were real. He knew of their existence since his adolescence (the signature in the letters to Grindelwald confirms this), but at some point in his life, he seemed to give up the search (if he ever really started looking for them in the first place).

In my opinion, the moment when Dumbledore starts to believe they are real is when he receives James Potter's cloak and runs tests on it. Upon realizing its special properties and knowing that James Potter is a distant descendant of the Peverell family, his doubts likely dissipated. When he finally found the ring (which I consider to be the strangest of the three Hallows), he was completely convinced.