In this story, Sherlock Holmes is hired by a man who turns out to be the king of Bohemia. The King is engaged to a woman from a royal family but he is afraid that her family will call off the wedding if they find out that the King was once connected to Irene Adler. She is an opera singer who is not at all royal. In fact, she is originally from New Jersey.
Holmes thinks he can find out where the picture is by making it appear that her house is on fire. He will then observe where she goes because she is sure to try to rescue the picture.
Irene Adler appeared in the first Sherlock Holmes short story "A Scandal in Bohemia." The King of Bohemia approaches Holmes and tells Holmes that he, the King, is afraid that Irene will reveal their previous relationship or blackmail him for money, since a photograph of them as a couple was taken, and he is now engaged to another woman. Holmes then goes to her home, and in p lan to discover the photo, finds out that she soon leaves for the US with the photo and has no reason to cause any harm to the King. Holmes later refers to her as "the woman" in other places in the series.