Advancements in emerging technologies, e.g., reconfigurable intelligent surfaces and holographic MIMO (HMIMO), facilitate unprecedented manipulation of electromagnetic (EM) waves, significantly enhancing the performance of wireless communication systems. To accurately characterize the achievable performance limits of these systems, it is crucial to develop a universal EM-compliant channel model. This paper addresses this necessity by proposing a comprehensive EM channel model tailored for realistic multi-path environments, accounting for the combined effects of antenna array configurations and propagation conditions in HMIMO communications. Both polarization phenomena and spatial correlation are incorporated into this probabilistic channel model. Additionally, physical constraints of antenna configurations, such as mutual coupling effects and energy consumption, are integrated into the channel modeling framework. Simulation results validate the effectiveness of the proposed probabilistic channel model, indicating that traditional Rician and Rayleigh fading models cannot accurately depict the channel characteristics and underestimate the channel capacity. More importantly, the proposed channel model outperforms free-space Green's functions in accurately depicting both near-field gain and multi-path effects in radiative near-field regions. These gains are much more evident in tri-polarized systems, highlighting the necessity of polarization interference elimination techniques. Moreover, the theoretical analysis accurately verifies that capacity decreases with expanding communication regions of two-user communications.