Hi Amit,
nice puzzle. :-)

Here's my answer: I think there is already a paradox in your first line.
If you really believe in something, then for you it is completely real and completely true. A person can't separate things which "really exists" from things which they only believe exist -- unless they don't really believe.

So you must be describing people who don't really know and don't really believe, but they are complicated anyway.
Does this help?

Suppose a friend of yours is suspected of stealing something. He looks into your eyes and tells you that he didn't do it. You tell him you believe him. Does your statement carry the same weight if you happened to see who really stole it?