If there are ten lottery tickets, and I hold one, I shouldn't hope to win, but I should simply assign probability 1/10 to my winning. Anything beyond the probabilities in the way of hope would be irrational. Likewise, if I have probability 9/10 of winning. Then I can have confidence, but this confidence should no more be a hope than in the former case. It's just a confidence of 9/10.
But if my friend has fallen morally many times but promises to do better, I shouldn't simply calculate the probability of his doing better using the best inductive logic and leave it at that. I should hope he will do better.
What makes for the difference? In the case of the friend, he should do better. But it is, of course, false that I should win the lottery. Indeed, the outcome of my winning the lottery is in no way normatively picked out. I can appropriately hope that the lottery will be run fairly, but that's that.
If this is right then it seems hope is of what should be. Well, that's not quite right. For if I have done something so terrible that my friend is under no obligation to forgive me, I can still hope for her supererogatory forgiveness. So, perhaps, hope is of what should be or what goes over and beyond a should.
If this is right, then this neatly dovetails with my account of trust or faith. Faith has as its proper object a present state of affairs that should be, such as a testifier's honesty and reliability, or perhaps—I now add—a present state of affairs that goes beyond a should. Hope has as its proper object a future state of affairs that should be or goes beyond a should. Both of these flow from love.
If this is right, then in order for there to be appropriate hope in things beyond human power—such as a hope that an asteroid won't wipe out all life on earth—there must be shoulds, or beyond-shoulds, that go beyond human power. This requires an Aristotelian teleology or theism.