Quantum Key Distribution (QKD) is a promising technology for secure communication, leveraging the principles of quantum mechanics to ensure the confidentiality of transmitted data. This paper explores the application of a probabilistic quantum key distribution (QKD) algorithm, employing a novel approach based on quantum entanglement and topology to provide a rigorous security proof. The core mechanism involves exploiting the inherent probabilistic nature of quantum systems to demonstrate the algorithm's resistance to eavesdropping. We provide a detailed mathematical framework and justification for the proposed proof, emphasizing the role of topology in shaping the security properties. This research aims to advance the understanding of QKD's security through a probabilistic framework, offering a distinct approach to guarantee secure key exchange.