Racing Car Finish Line

Options
I'm creating a very fast paced racing game.
If 2 cars are really close to each other, one of the cars are in first in the server, but for the second place car on ther own machine he see his car in first place. What should I do when he finishes the race? Put him in a second place even he thinks he was in first or put the two players in first since probably they will never see each other in real life.
Or there is another option?