Electric vehicles (EVs) are believed to play an important role in mitigating carbon emissions in the transportation sector. However, EVs may still cause carbon emissions in the power sector if they are charged by electricity generated from burning fossil fuels like coal. Researchers have focused on managing emissions on the power generation side. However, the underlying driver of carbon emissions is the demand of consumers. To this end, a probabilistic carbon footprint management strategy is proposed for EVs in this paper. First, the conventional deterministic carbon emission flow model is extended to a probabilistic one (PCEF) to track the carbon footprint of EVs considering various uncertainties based on non-intrusive load monitoring (NILM) and the two-point estimation method (2PEM). Second, a stochastic chance-constrained carbon footprint management model for EV charging is proposed to address the carbon obligation allocation of EVs from the perspective of consumption and provide a technical basis for demand-driven stimulation to reduce carbon emissions. Third, a solution methodology is proposed to solve the formulated chance-constrained problem based on nonparametric Bayesian modeling and inference. The proposed model and methodologies are verified on the IEEE 39-bus system. The feasibility of the proposed PCEF model is validated. According to the simulation result, the computation speed of the proposed PCEF model is improved from 3456.8 seconds to 1341.3 seconds compared with the Monte Carlo simulation by sacrificing the accuracy within 2%. Besides, the proposed emission control strategy can realize a better emission control performance compared with the other state-of-art works. Compared with the base case, the total emission is reduced by 82 tons annually, and the emission reduction rate is increased by nearly twice.