It doesnt look pretty as she uses to look often but show a different aspect of Alexandra that i like. In this picture we can see she wasnt all the time that woman with melancholic and kind of bitter look and that makes her more "close", at least to me, someone who never liked her.
Sometimes we forget that some people (AKA famous people, royals, etc) are (or Were ) Humans, not perfect and flawless people 24/7 . This is what a normal (cheerie and happy) people does in a private context ; fool around and being silly at the camera.