Ride-sharing is increasingly recognised as a potential solution to transportation issues such as traffic congestion and parking problems. The success of ride-sharing systems depends on the willingness of individuals to share rides, and effective pricing strategies are among the crucial factors. However, creating a fair pricing system for riders and providers remains challenging. This research introduces a new pricing scheme based on the concept of shareability. This concept considers all the possible sharing situations among trips. It is designed to incentivize riders and accommodate providers' criteria. This scheme calculates the trip fare for passengers, considering various ride-sharing scenarios derived from the shareability function, thus ensuring fairness and transparency for passengers. Using the macroscopic fundamental diagram, our model incorporates traffic dynamic conditions. We have applied the method to the real case of Lyon city in France to assess the effectiveness of our approach. Through a comprehensive analysis of various configurations of the proposed pricing scheme and benchmarking with the existing approaches, we demonstrate its superior performance in reducing ride rejections compared to traditional methods. This result showed the proposed method's potential for enhancing ride-sharing systems' effectiveness.