I don't understand, how does that make it rational to believe Harry might be real?
It's rational to recognize that Harry Potter's unreality is unproven.
How much effort you put into proving Harry Potter's unreality, and how much effort you put into justifying your belief one way or the other, is purely a question of what standard of evidence you wish to apply. That is completely separate from where the burden of proof lies in relation to the claim that Harry Potter is not real.
If you were to tell me "Harry Potter is not real", I'd happily agree with you. Not because you've successfully avoided a burden of proof (you haven't), but because neither of us thinks this claim requires a very high standard of evidence at all. Your burden of proof is already met, to both our satisfaction, right out of the box.
If you were to ask me to accept the claim "God is not real", on the same basis as the claim "Harry Potter is not real", fine. But we should still at least understand what that basis is. We still have to acknowledge that the claim has a burden of proof. We still have to establish what standard of evidence we're going to apply, and what evidence was produced to meet that standard.
Nobody bothers to examine the claim that Harry Potter isn't real, because nobody really gives a **** about that. We have the provenance of a fictional Harry Potter character, and that seems to satisfy just about everybody
On the other hand, a lot of people care a lot about the claim that god isn't real. So all the rational stuff that we don't feel the need to bother with, when it comes to Harry Potter claims, has to be bothered with when it comes to God claims.