Dic: reason to do something (one of its meanings as a noun)

• There is reason to believe that the accused did not commit this crime.
• They had reason to believe there could be trouble.
• He had every reason to be upset.

[The American Heritage] 3.

An underlying fact or cause that provides logical sense for a premise or occurrence:

[Cobuild] 2. N-UNCOUNT : usu N to-inf.

If you say that you have reason to believe something or to have a particular emotion, you mean that you have evidence for your belief or there is a definite cause of your feeling.