Let us define "fastness" as a characteristic of how fast/agressive a driver is. One aspect of this is the (maximum) time between a traffic light turning red and the driver deciding they have to stop. The assumption here is that a "slow" driver will have low (read: very negative, like minus 5 seconds) value because they start stopping as soon as they notice the orange traffic light. On the contrary, a "fast" driver will have a higher value, like -1 second or even a positive one like 3 seconds, being "a bit" illegal.
(Disclaimer: fast and slow, as words, tend to give a positive "taste" on fast rather than slow. I chose them because they have few letters, and I do not advocate dangerous driving!)
By using this "time from red light to stop" as a random variable X, let's assume a normal distribution of drivers with known parameters m(average) and v(variance).
If that is so, what is the probability distribution that, when being stopped at a red light yourself, the driver at the frontmost of the queue is X-fast?
I guess slow drivers are more probable to appear there because they stop more easily/frequently. The logic behind the solution is more important than formulas here, and that is why I chose to post this here instead of math.se .