One function that works for this is log scoring: the number of points you get is the log of the probability you place in the correct answer. The general thing to google to find other functions that work for this is "log scoring rules".

At the Australian mega-meetup, we played the standard 2-truths-1-lie icebreaker game, except participants had to give their probability for each statement being the lie, and were given log scores. I can't answer for everybody, but I thought it was quite fun.