The correct option is C Sadly, the king showed little justice to the pauper.
'A little' is a quantifier that means 'a small amount of'. If the king had shown 'a little' justice, the sentence would not have begun with the adverb "Sadly...", it means 'unfortunately', it wouldn't have been unfortunate if at least a little justice was shown. By eliminating the article 'a' the meaning of the sentence changes, making it sound more correct, as 'little' means 'almost negligible. Option A is incorrect because 'the' modifies specific nouns, whereas 'justice' is not specific here. Since option B is correct in meaning that it was unfortunate that almost no justice was shown to the pauper, option B is correct. Replacing 'some' does not change the meaning of the original sentence that we're given, by saying that giving some justice to the pauper was unfortunate it's the opposite of what the sentence means, hence option C is also incorrect.