Faith in God and intuition

From the rabbi’s words, I understand the following picture – belief in God is a claim of fact that relies on reasoning. While it is uncertain and cannot be scientifically tested, it is still much more plausible than any other theory and therefore should be adopted.
The thing is, I’ve seen in several places that the Rabbi connects faith in God with intuition. I don’t understand what the connection is between the concept of intuition and the above picture. Why is it needed and what does it add? Thanks.