The likelihood that the belief you are born with is correct

Hello Rabbi.
This is a question I've been thinking about recently, it mixes a little philosophy, a little psychology, and a little mathematics I guess – three subjects I don't understand at all, so I'd love to hear your opinion.
It is clear to me that no matter how much a person tries to investigate beliefs in a purely rational way, they are still significantly influenced by the environment they were born into and the beliefs their parents believe in, and I assume you would agree with that. In addition, I know that there are many, many different religions around the world – a very large proportion with a much larger number of believers than Judaism. So I wonder – what are the chances that you will be born into exactly the right religion? Especially if it is a small religion like Judaism, assuming that you have come to the conclusion that it is the right religion, isn't it more likely that psychological influences caused you to choose this path than that a miracle actually happened and you were born into exactly the right religion?
I'm aware that this is not an argument against the Jewish religion (there must be some kind of argument that describes this fallacy), but I still don't see why this doesn't mean that Judaism should be placed last in terms of the chance that it is true (and in any case, the evidence in its favor would have to be much stronger than usual)…