The characteristics of large-scale stochastic output of renewable energy in the new power system have posed a risk of failure in the current online transient stability assessment results. This issue simultaneously challenges existing methods in terms of component modeling accuracy, system topology adaptability and computational speed. In this study, a novel approach is proposed that combines improved confidence band method based on re-probability and a probability distribution and confidence band evaluation model of stable index based on graph deep learning. The graph deep learning model rapidly evaluates a few sampled points, which are then expanded using the confidence band method based on re-probability. Temporal domain simulations are guided by co-occurrence knowledge from labeled data to enhance accuracy. Finally, the confidence band calculation method is employed to derive the stability probability distribution and assessment conclusion in intervals under stochastic output conditions. The method capitalizes on the topological adaptability and rapid computation inherent to graph deep learning. Moreover, it remains unhindered by limitations in component modeling accuracy. The conclusions drawn from the confidence band calculation are firmly rooted in theory and can evaluate the stable probability distribution. Evaluation accuracy verification on the IEEE-39 and IEEE-300 bus systems demonstrates the efficacy of the proposed method in accurately predicting specified transient stability indices and delivering reliable probability assessments.