"I have no proof, nor even an expectation that there is any connection."
It depends on what you are trying to say, but I think perhaps 'credulity' misses the mark slightly, and 'gullibility' completely. I connote that these words are intended to convey general properties of the individual and not his reaction or state in a particular circumstance.
"I have no proof of a connection, nor even the weakest evidence. I have, in fact, no rational reason whatever to believe that such a connection exists," or, more simply "I have no justification for believing a connection exists, or simpler still, "There is no indication of a connection."
What sense are you trying to convey? That there really is no connection between these things and one should not believe that a connection exists, or that you believe there is a connection, even though you have no rational justification for your expectation?
