Aiming at the vertical generation cost-differentiated electricity market prevailing after carbon emission reduction and significant difference in large user's generation capacity preference, the paper proposes probabilistic supply of electric quantity and its corresponding probabilistic generating, and utilizes price leverage to regulate insufficient generation opportunity and supply efficiency of low-carbon generation, especially high generation cost generation. The probabilistic generating models under endogenous and exogenous choices of generation cost are constructed successively, the generator's electric quantity supply equilibria are solved, and the optimality of probabilistic generating strategies is analyzed. Finally, the model under endogenous generation cost choice is extended to the probabilistic generating model which decomposes the market demand uncertainty. The research finds that probabilistic generating can be regarded as a way to profitably dispose excess capacity compared to three generating benchmarks, and remains viable even when the generation cost choice is endogenous. When the generator employs generation strategy of “strong” cost differentiation, the introduction of intermediate probabilistic generating causes closer cost levels in a product line, and enhances the large user's consumer surplus. In contrast, in the market where the generator implements generating of “weak” cost differentiation, the use of probabilistic generating increases cost separation and degrades the large user’s consumer surplus. Under the uncertain market demand, when the large user preferring lower cost generation capacity has a relatively high taste for generation cost relative to the large user preferring higher cost generation capacity, probabilistic generating may arise as a tool to manage adverse demand conditions.