Carbon emission flow is an effective tool to obtain carbon emission distribution in power systems, which can guide the active carbon reductions of consumers through proper incentive schemes. With the increasing penetration of renewable energy, the existing single-valued carbon emission flow model based on deterministic forecasted power outputs cannot describe the impacts of renewable energy uncertainties on carbon flows. Therefore, this paper mainly focuses on the assessment of the probabilistic carbon emission flow through the power systems considering the impacts of load and renewable energy uncertainties. In this paper, the probabilistic carbon emission flow (PCEF) is innovatively proposed. With the PCEF, consumers can make better energy use plans considering their own risk appetites for carbon emission payment. Firstly, the impact factors of the PCEF are modeled, including load and renewable energy uncertainties and integrated carbon intensity of thermal plants. The uncertainties of load, wind power and photovoltaics are modeled based on a p-box method while the uncertainty of hydropower is modeled based on the multi-state model. Besides, the integrated carbon intensity model of thermal plants are proposed considering the carbon intensity variations during the operating, start-up, and shut-down stages. Furthermore, the probabilistic carbon emission evaluation framework is proposed to assess the probabilistic carbon distribution. In this framework, novel probabilistic carbon indices are defined to precisely characterize the carbon emission situation with probabilistic representations. A solution method based on an adaptive interval point estimation (AIPEM) algorithm is proposed to efficiently solve the developed evaluation problem. Tests on an IEEE-30 node system, and a real provincial power system in China validate the effectiveness and application of the proposed model. The results showed that the PCEF can be a useful tool for obtaining the probabilistic representation of carbon emission flow and guiding the consumers’ active carbon reduction in power systems.