With the emergence of e-commerce, the recommendations provided by commercial platforms must adapt to diverse scenarios to accommodate users' varying shopping preferences. Current methods typically use a unified framework to offer personalized recommendations for different scenarios. However, they often employ shared bottom representations, which partially hinders the model's capacity to capture scenario uniqueness. Ideally, users and items should exhibit specific characteristics in different scenarios, prompting the need to learn scenario-specific representations to differentiate scenarios. Yet, variations in user and item interactions across scenarios lead to data sparsity issues, impeding the acquisition of scenario-specific representations. To learn robust scenario-specific representations, we introduce a Global-Distribution Aware Scenario-Specific Variational Representation Learning Framework (GSVR) that can be directly applied to existing multi-scenario methods. Specifically, considering the uncertainty stemming from limited samples, our approach employs a probabilistic model to generate scenario-specific distributions for each user and item in each scenario, estimated through variational inference (VI). Additionally, we introduce the global knowledge-aware multinomial distributions as prior knowledge to regulate the learning of the posterior user and item distributions, ensuring similarities among distributions for users with akin interests and items with similar side information. This mitigates the risk of users or items with fewer records being overwhelmed in sparse scenarios. Extensive experimental results affirm the efficacy of GSVR in assisting existing multi-scenario recommendation methods in learning more robust representations.