I see nothing in the Constitution about ‘runners up’.
The constitution provides a line of succession:
President
Vice-President
Speaker of the House
It would be a fight in any event. Biden would likely be excluded because he was on the ticket with Pbama who would be disqualified and deposed. Pelosi would be challenged and possibly forced out because she had direct responsibility to certify Obama as qualified.
The country would be in an uproar. I can’t see anything short of calling a special election. I believe the winner of the special election would serve the remainder of the vacated term.
There is no constitutional provision for Special elections. It would not happen.