Accommodating a high penetration of intermittent photovoltaic (PV) in distribution systems can potentially cause several operational problems, most importantly, voltage violations. An optimal probabilistic approach is proposed in this article to optimally host high penetrations of PV units considering their stochastic nature. A benefit of the proposed approach is that it provides wider planning options since it optimizes the interfacing inverter oversize with smart watt-var functionalities. These smart functionalities include: 1) active power curtailment and 2) inverter reactive power. The utilization of these functionalities in the optimization model yields an optimal PV hosting that maximizes the benefits to distribution systems. The optimal probabilistic model of PV incorporates the probabilities of the PV power output and load while optimizing the inverter oversize and the two functionalities simultaneously. The proposed approach complies with the recently released IEEE 1547:2018 standard which regulates the reactive power support via the interfacing PV inverters. The efficacy of the proposed approach is demonstrated by comparisons with existing approaches. The results confirm the superiority of the proposed approach to optimally accommodate high PV penetration at single or multiple locations while minimizing voltage violations. The proposed approach is also applied to maximize the hosting capacity of PV.