Can you actually have a policy in place for this?
Policy for Termination During Probation
Can you have a policy that states, since you are on probation, you will be terminated in case of an accident that was not your fault, was an act of God, or completely the fault of a jerk driving drunk on that day? Since the driver is on probation, there is nothing in the law preventing the termination of the driver during the probation period (we are not talking about denying compensation related to the accident, right?). However, if it was not his fault, is that fair? More importantly, perhaps, are you losing a good driver for no fault other than that he was on probation?
Determining Fault in Accidents
How do you determine whose fault it was? Mostly you will believe the passenger he was carrying. Or if you have GPS devices fitted that tell you what speed he was driving, it will give you a good idea.
Impact of a Strict Policy
Take a different view now: Suppose you make a policy stating that any driver having an accident during probation will be terminated. So every new driver will drive VERY carefully during the probation period. He will probably drive slower than necessary, causing delays and probably damaging the car due to excessive driving in a lower gear. Once he is out of probation, he will start speeding and acting recklessly, maybe out of pent-up frustration from the previous periods.
I would say you do not need a policy. Instead, you need to take each case on its merits and decide.