Somsak：May I bring you a salad?
Susan：Oh yes. What do you recommend today?
Somsak：I recommend rose-petal salad. Special for new friends.
Susan：[to Harry] Rose-petal salad?
Somsak：I'll take care of everything. [He leaves.]
Susan：I hope you're hungry.
Harry：What? Oh, yes. Starving.
I find this explanation in a dictionary:
- (tr; takes a clause as object) to trust, expect, or believe: we hope that this is satisfactory.
Dose hope in my example sentence mean to believe? If that is the case, instead of using believe or think, why would one use hope here? Is there any difference in nuance between them?