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The interactions between a range of large-scale climate oscillations and their quantitative links with precipitation are basic prerequisites to understand the hydrologic cycle. Restricted by the current limited knowledge on underlying mechanisms, statistical methods (e.g. correlation methods) are often used rather than a physical-based model. However, available correlation methods generally fail to explain the interactions among a wide range of climate oscillations and associated effects on the water cycle. This study presents a new probabilistic analysis approach by means of a state-of-the-art Copula-based joint probability distribution to characterize the aggregated behaviors for large-scale climate patterns and their connections to precipitation. We applied this method to identify the complex connections between climate patterns (westerly circulation (WEC), El Niño-Southern Oscillation (ENSO) and Pacific Decadal Oscillation (PDO)) and seasonal precipitation over a typical endorheic region, the Tarim River Basin in central Asia. Results show that the interactions among multiple climate oscillations are non-uniform in most seasons and phases. Certain joint extreme phases can significantly trigger extremes (flood and drought) owing to the amplification effect among climate oscillations. We further find that the connection is mainly due to the complex effects of climatic and topographical factors.