Answer:
The given question refers to the short detective story The Purloined Letter written by Edgar Allan Poe. The protagonist, detective Dupin, has to solve a case - Minister D stole a letter from the queen's lover from her boudoir and is not blackmailing her.
We are not told why everyone acts as if they are uninterested in the contents of the letter. Still, we can conclude that the letter is from a lover, because it arrives in the queen's bedroom (indicating that the one who wrote it must be someone very close to her as they had access to her boudoir), and she particularly wants to hide it from her husband. That's why we can assume that the scandal is sexual in nature.