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Multi-energy industrial parks, composed of the district energy supply system and terminal industrial loads, are dominant energy consumers with over 50% occupation of total energy consumption. Considering the energy conversion in the district energy supply system and adjustment of production subtasks in terminal industrial loads, the industrial parks could provide considerable flexibility for utility multi-energy systems to deal with contingencies. However, industrial parks may have multiple uncertainties originating from the production subtasks' variability, distributed renewable energy's fluctuation, and random failures of equipment. These uncertainties could make the flexibility assessment of industrial parks unreliable, which may further exacerbate utility system risks. To address the problem, this paper innovatively proposes the concept of probabilistic integrated flexible regions and corresponding characterization approaches, which can effectively describe the credible multi-energy adjustment ability of industrial parks. First, the energy-material flows in the industrial park are modeled considering multiple uncertainties while subject to constraints such as operating limits of equipment, energy and material balancing, and production targets. Then, the modeling and calculation methods of probabilistic integrated flexible regions are given. These regions are labeled with certain probability requirements and visualized in the input multi-energy space. Using a real-world test system that produces air conditioning equipment in China, the results show that the proposed model can effectively reflect the probability characteristics of the integrated flexibility under multiple uncertainties. For this test system, the area of a highly credible integrated flexibility, represented by the probabilistic integrated flexible region with 99% probability, is about half of that obtained by the deterministic model. That is, half of the integrated flexibility evaluated by the deterministic method in the test system may not be practically utilized considering the impacts of uncertainties. Therefore, the proposed method could provide a credible and comprehensive evaluation of the multi-energy industrial park's flexibility considering multiple uncertainties.