If you want to modify the probability based on karma points, I would suggest giving larger probability to those users with fewer points, as those with more points (ostensibly) would already get more attention given to their submissions anyway.

Dave won't get anywhere with either this scheme or the one I proposed, at least not immediately. But that's the idea: it will be a little bit harder for Dave to gain traction, but it will demonstrate that he's not a spammer, which should be a reasonable price to pay for ensuring the site isn't overrun with garbage (any more than some claim it already is).