Robust belief revision methods are crucial in streaming data situations for updating existing knowledge or beliefs with new incoming evidence. Bayes conditioning is the primary mechanism in use for belief revision in data fusion systems that use probabilistic inference. However, traditional conditioning methods face several challenges due to inherent data/source imperfections in big-data environments that harness soft (i.e., human or human-based) sources in addition to hard (i.e.,

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... sensors. The objective of this paper is to investigate the most natural extension of Bayes conditioning that is suitable for evidence updating in the presence of such uncertainties. By viewing the evidence updating process as a thought experiment, an elegant strategy is derived for robust evidence updating in the presence of extreme uncertainties that are characteristic of big-data environments. In particular, utilizing the Fagin-Halpern conditional notions, a natural extension to Bayes conditioning is derived for evidence that takes the form of a general belief function. The presented work differs fundamentally from the Conditional Update Equation (CUE) and authors own extensions of it. An overview of this development is provided via illustrative examples. Furthermore, insights into parameter selection under various fusion contexts are also provided.