The emergence of distributed generation has become significant over the last few years, bringing several challenges to traditional grid-connected electricity distribution systems. Technical limitations of integrating these new renewable distributed generation to the existing electricity grid made new avenues to change the way of energy consumption, which converted traditional consumers to prosumers. Peer-to-peer energy trading platforms enable these prosumers to trade electricity with their neighbours in microgrids where new electricity markets emerge with new technologies. This research introduces a concept of peer-to-peer energy trading for grid-connected electricity distribution networks. In its initial phase, the study models prosumer load sharing for households equipped with solar PV and battery energy storage. This modelling employs a Markov chain, where energy share states are determined by parameters in a Markov transition probability matrix. These parameters are varied during different time intervals of the day, reflecting varying cost components under a Time-of-Use (TOU) tariff structure. This approach enables prosumers to meet their load demand cost-effectively, fostering engagement in peer-to-peer energy exchanges. The proposed Markov model is simulated with 15-minute spot pricing intervals, demonstrating effective management of prosumer load demands in the peer-to-peer market environment, showcasing the potential benefits of this innovative energy trading approach.