Although carbon flow is a powerful tool for assigning emission responsibility to consumers, it has not been explored in hybrid AC-DC systems. This paper presents a novel probabilistic carbon-flow model to quantify the distribution of carbon intensity in such systems. To further characterize the importance of uncertain inputs, such as renewable energy and loads, on probabilistic carbon flow, a global sensitivity analysis (GSA) strategy is introduced. To alleviate the computational burden of traditional Monte Carlo methods in quantifying these metrics, it incorporates an adaptive polynomial chaos expansion (PCE)-based surrogate model. This significantly reduces the computing burden while maintaining high statistical accuracy. Simulations validate the proposed carbon flow model in the hybrid AC-DC system and reveal the excellent performance of the PCE-based GSA method.