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The deterministic nature of conventional precipitation data sets complicates their utility in applications. The underlying estimation principle (minimizing errors) involves biases in extremes, and conventional uncertainty quantification (cross-validation) is impractical. We present a method to derive spatial analyses of daily precipitation, probabilistically, as an ensemble, conditional on the available rain gauge data. The method builds on and extends previous techniques using conditional simulation with Gaussian Random Fields. The extension involves trans-Gaussian and piecewise covariance modeling to let the ensemble respond to regional precipitation conditions, Bayesian inference to account for parameter uncertainty, and simulation on a primary grid to ensure the ensemble has a well-defined areal support. While addressing prevalent issues of existing techniques, our method involves a compromise in global consistency that limits the utility of the ensemble over large domains. We apply the method to derive ensembles of area-mean precipitation for hydrological area units in the Alps. The ensembles are demonstrated to plausibly capture variations in uncertainty with rainfall condition, rain gauge density, and averaging area. Evaluations suggest that the probabilistic estimates are internally consistent and of good statistical reliability. There is a tendency to underestimate uncertainty for light precipitation. Results point to remarkable uncertainties, even with the dense gauge networks in the Alps: For means over 500-km(2) areas we find the ensemble spread to be typically a factor of 2-4 (factor of 1.5) for intense convective (stratiform) events. This also implies nonnegligible uncertainty in climate indices. Probabilistic representation of interpolation uncertainty in spatial data sets allows users to track them into applications.