We present a novel framework that enhances 3D Gaussian Splatting (3DGS) with improved computational efficiency and relighting capabilities through probabilistic optimization. While 3DGS enables real-time, high-quality scene reconstruction and rendering, it remains limited to static lighting environments and suffers from redundancy due to millions of Gaussians. To address these limitations, we introduce a Markov Chain Monte Carlo (MCMC)-based approach that adaptively prunes redundant Gaussians while preserving critical details. Our contributions include MCMC-based adaptive thresholding, surface normal learning for realistic shading under dynamic lighting, and gradient-guided light sampling via the Metropolis-Adjusted Langevin Algorithm (MALA). Experimental results demonstrate that our proposed method achieves significant memory reduction and faster convergence, enabling real-time relighting with fewer Gaussian primitives.