Definition of Hope - 1
: to desire with expectation of obtainment
: to expect with confidence : trust
To expect with confidence implies there is a reason that confidence is there. Like "I hope you get better". I wouldn't say that to someone who had a terminal illness. However a person who has a cold, and evidence shows most people get better from a cold, would be a more appropriate time for me to say "I hope you get better".
Example "I hope I get that raise". I wouldn't say that if there wasn't something to back that. So do I "Believe in" hope. No hope is not something I "believe in". Hope is something I do by backing it with something substantial.