Joe Biden was 26 then, fresh out of law school with the Delaware bar exam behind him, and a Michel Legrand song began playing on the radio of his Corvette Stingray roadster. It was called “What Are You Doing the Rest of Your Life?” and even for a young man with a capacious ambition, he couldn’t have imagined the course his life would take.There were, as the 1969 song projected, tom...