What is evidence? If you watch murder mysteries then often evidence is purely circumstantial, and it takes a real battle of wit to find the evidence that irrevocably pinpoints the murderer or puts him or her squarely at the place of the murder at the exact time.
Evidence is needed to convince people in the "normal" world, but when it comes to matters beyond proven science then belief starts becoming more important. It is like belief is when your intuition tells you what the real truth of the matter is.