Just as 'defeat' is related to 'victory', in the same way what is related to…

Concept: A word-pair analogy holds only when the SAME relationship that links the first pair links the second. Here 'defeat' and 'victory' are direct antonyms (opposite outcomes of a contest), so the relationship is ANTONYM.

1. Identify the relationship in the given pair: defeat is the opposite of victory.

2. Apply the same antonym relationship to 'despair': find the word that means the opposite of despair (a feeling of hopelessness).

3. The opposite of despair is hope, the expectation that things will turn out well. So despair : hope mirrors defeat : victory.

Cross-check: substitute back — 'defeat is to victory as despair is to hope' reads as one antonym pair mapped onto another, confirming the match.