Speaking of Dukes of York - The last two Kings were Dukes of York who were not expected to inherit the throne.*
Considering the current Duke of York, that's a little scary.
*George V's older brother died before his father, and George VI's brother abdicated. Neither had children. Since the current Prince of Wales has William and Henry, I doubt it will be a problem. Still...it is scary.
I see that someone's already beaten me to the correction that it was two out of the last three kings: King Edward VIII (later the Duke of Windsor) was Prince of Wales, not Duke of York, prior to becoming King.
Interesting fact about King George V's older brother (Albert Victor, Duke of Clarence): at the time of his death, he was engaged to be married. (Can you imagine if Wills had died before the wedding?) What is a young woman to do when she's engaged to the heir to the throne, but he dies unexpectedly? Why, get engaged to his younger brother, who's now the new heir! That's what Albert Victor's fiancee did! Her name was Princess Victoria Mary Augusta Louise Olga Pauline Claudine Agnes May, known as May -- and later, of course, Queen Mary.