Biden didn't run b/c he had just lost his son and the grief took priority. It was very likely he would run before that happened.
"I had planned on running before Beau got sick. I have great respect for Hillary [Clinton]. She would have made a hell of a president. But I thought I was far and away the most qualified person to finish the job Barack [Obama] and I started.
When Beau got sick, Beau was absolutely insistent that I not let anybody know. The people who had begun to organize for me, if I had told them, “Stop,” they would have known we didn’t expect Beau to live. So this developed into people thinking the reason I wasn’t running [was] because I was worried about Hillary."
https://www.latimes.com/opinion/op-ed/la-ol-patt-morrison-joe-biden-20180116-htmlstory.html