The correct option is A Little
'Little' means 'not much' or 'negligible' as a quantifier to the noun 'hope'. It's mentioned here that 'he' would not be able to make a complete recovery, hence we use 'little' as there is not much hope. Hence option B is correct. 'A little' is a positive quantifier, meaning it denotes a small quantity or amount of a noun. Since the sentence calls for a negative quantifier because it's given that there's almost no chance of a complete recovery, option A is incorrect. 'The little' is a quantifier that modifies a noun that is specific, since the noun 'hope' is not specific, option C is incorrect. 'Few' is used for countable nouns, since hope is not countable, option D is incorrect.