It's of a type which you wouldn't believe.
Why do you believe in it?
Because it happened to me.
Whether you're a hyperskeptical empiricist or gullible naive fool, all evidence derives from your senses. Even evidence experienced by others and reported to you has to travel past your eyes/ears before you get to decide whether or not to believe.
What personal experience could happen to a person to make the existence of God unequivocally the known answer and drive out much better established explanations?
For me, it would be something like, "if a God could completely stop hunger, disease and crime for one full week, I would be unable to draw any conclusion other than the supernatural to explain it." Of course, for someone to claim that Supernatural being was Yahweh "him"self, I would need more. Like, "Globally, the pages of all religious texts other than the correct translation of the bible were to go blank for one month," (to give time to verify), then that would be pretty convincing and would have no more-likely explanation to use.
You'll note that nothing would convince me in any way if I were the only one to know about it. An hallucination would be a much more probative answer