The scenario we're talking about is that you have had an experience, that you cannot explain other than by positing that you had a random hallucination on a normal day.
The rational thing to believe is that you're either ignorant, or you have had a random hallucination on a normal day.
If it's possible to use rationality to rationally prove that rationality does not universally apply, you would have a rational explanation for the same. Otherwise, to believe in the non-rational is simply irrational.
If I have two oranges in my refrigerator, and I put two more in, I should have four oranges. If I open it up and see three oranges, I assume one was taken, or that I cannot find one, or something. If I find five, I assume someone else put oranges in my refrigerator, or something along those lines. If I rule everything out, before concluding that two plus two is three or five today for no reason, I'm even willing to entertain crazy theories such as that oranges occasionally merge or split.
Maybe I'm just crazy, and maybe it's just faith, but I somehow think there should be a rational explanation for why I find three oranges instead of the four I expect, and I happen to want to call this belief rational, since it is regarding rational explanations.