Plug-in electric vehicles (PEVs) are a sustainable choice in response to electrification and decarbonization policies. Their widespread adoption poses challenges and opportunities, particularly for distribution systems (DSs). This study introduces a comprehensive probabilistic method to assist DS operators (DSOs) in infrastructure decision-making under uncoordinated PEV charging scenarios. Using real-world case studies and employing a Monte Carlo-based approach, it evaluates the impact of PEV charging on various aspects of DSs, including voltage magnitudes, imbalance, technical losses, and transformer loading. Mitigation strategies are explored through adjustments of substation transformer tap settings, modifications of no-load tap changers (NLTCs), and installation of low voltage regulators (LVRs). Results indicate that while transformer tap adjustments can improve voltage profiles, NLTC modifications may worsen overvoltage issues. In contrast, LVR implementation significantly reduces the number of customer units with voltage violations and lowers daily compensation costs. However, relying solely on LVRs may be insufficient when PEV penetration exceeds 35%. Moreover, their effectiveness in mitigating voltage imbalance diminishes due to independent LVR control and increased load. Still, economic analysis shows that LVRs can be financially viable even under these conditions. Sensitivity analyses highlight the critical influence of both PEV penetration levels and their spatial distribution within the DS in realistic PEV modeling simulations. In conclusion, this study proposes a probabilistic method to assist DSOs in the decision-making process of enhancing voltage regulation on DSs, comprehensively addressing losses, voltage imbalances, and loading in DSs impacted by PEV adoption.