In the increasing traffic scenario and the presence of automated four-wheeler vehicle-like situations, we need to consider the possible safe driving for the two-wheelers also. As two-wheelers need manual balances, embedding the autopilot systems is a tougher task. To resolve this issue, we attempt to address this problem with probability spaces. Then, these classical probability spaces are promoted into quantum probability spaces. The quantum computing aspects such as quantum gates are embedded in the analysis of the quantum probability space. With those quantum computing protocols, various traffic scenarios are calculated, such as the probability of accidents and the avoidance probability of accidents. A set of mathematical lemmas with certain conditions and their proof for mapping classical to quantum probability space and the singularities in this quantum probability space are also discussed in this work.