Hebrews 11:1 states that "Faith is the assured expectation of things hoped for, the evident demonstration of realities, though not beheld." The Greek word rendered "assured expectation" was commonly used in ancient business papyrii to convey the idea of something that guarantees future possession. (A title deed, for example.)
The Greek word translated "evident demonstration" has the idea of presenting evidence to demonstrate something, especially something contrary to what appears to be the case. Evidence, Assurance, legal guarantee, are all ideas present in Hebrews 11:1.
The Bible presents abundant evidence to convince one that what God says is true, and the hope he gives is real and certain. A person who chooses to ignore such evidence cannot please God. (Hebrews 11:6)
A person whose car is reported stolen and who is stopped by the police can prove he is the car's owner by producing the title, and evidence that he is the person listed on the title. The police would not take the driver's word that he is the car's owner, for that would be blind credulity. Rather, based on the evidence presented, the police officer is assured, has convincing evidence of the driver's ownership. That assurance is what real faith is.