Today's strongly positive meaning dates from Anglo-Saxon times, but in the 13th century an alternative usage emerged which lacked the sense of desire, and this was still present in Shakespeare's day.
This new sense was more matter-of-fact, meaning "expect" or "envisage".
Without being aware of it, we cannot make sense of Innogen when she says, of the Queen, "She's my good lady; and will conceive, I hope, But the worst of me" (Cymbeline, II.iii.152).
She hopes the Queen will think of her badly? No, she means only that she expects the Queen will do so.
Hope as a noun also retained a more neutral sense, of "likelihood, possibility".
This is needed when Mistress Ford says to her friend, about Falstaff, "Shall we ... give him another hope to betray him to another punishment?"
(The Merry Wives of Windsor, III.iii.183). Falstaff can hardly be hoping (in the modern sense) for punishment.
David Crystal is author, with Ben Crystal, of Shakespeare's Words, published by Penguin. A subscription website is now available at www.shakespeareswords.com