A novel financial metric denominated unit financial impact indicator (UFII) is proposed to minimize the payback period for solar photovoltaic (PV) systems investments and quantify the financial efficiency of allocation and sizing strategies. However, uncontrollable environmental conditions and operational uncertainties, such as variable power demands, component failures, and weather conditions, can threaten the robustness of the investment, and their effect needs to be accounted for. Therefore, a new probabilistic framework is proposed for the robust and optimal positioning and sizing of utility-scale PV systems in a transmission network. The probabilistic framework includes a new cloud intensity simulator to model solar photovoltaic power production based on historical data and quantified using an efficient Monte Carlo method. The optimized solution obtained using weighted sums of expected UFII and its variance is compared against those obtained by using well-established economic metrics from literature. The efficiency and usefulness of the proposed approach are tested on the 14-bus IEEE power grid case study. The results prove the applicability and efficacy of the new probabilistic metric to quantify the financial effectiveness of solar photovoltaic investments on different nodes and geographical regions in a power grid, considering the unavoidable conditional and operational uncertainty.