Determining the at-fault party depends on prima facie (at first sight) evidence. In legal contexts, prima facie evidence is enough to prove a particular fact or element of a case.
If the driver can show proof the other party failed to yield, it would help the court decide who has liability. However, suppose this evidence does not exist. In that case, an experienced lawyer can build the case to argue against the driver at fault's behavior.
For example, you can show evidence of speeding, driver distraction, or driving under the influence. That is enough to prove liability.
However, assigning responsibility in personal injury cases is rarely simple. Car accident lawyers may work with an accident reconstruction specialist to determine liability.