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With the sharp increase in fluctuant sources in power systems, the deterministic power flow (DPF) calculation has been unable to meet the demands of practical applications; thus, the probabilistic method becomes indispensable for the reliable and stable operation of power systems. This paper adopts the probabilistic power flow (PPF) method, which is a Monte Carlo simulation (MCS) based on the Latin hypercube sampling (LHS) method, to analyze the uncertainties of power systems. Specifically, the available load supply capability (ALSC) based on the branch loading rate is used to analyze the safety margin of the whole system, while the improved power flow entropy is introduced to quantify the equilibrium of power flow distribution. The repeated power flow (RPF) calculation is combined with the PPF method, and, hence, the probabilistic repeated power flow (PRPF) method is proposed to calculate the power flow entropy at the initial state and the probabilistic ALSC. To flexibly control the power flow, the unified power flow controller (UPFC) is added to the AC power system. The different control coefficients of UPFC are set to reveal the relationship between power flow entropy and available load supply capability under the stochastic scenarios. Finally, the modified IEEE14 test system is used to study the adjustment abilities of UPFC. With consideration of uncertainties in the test case, the positive effect of UPFC on the power flow entropy and the probabilistic ALSC under stochastic scenarios is deeply studied.