Weak lensing measurements are starting to provide statistical maps of the distribution of matter in the universe that are increasingly precise and complementary to cosmic microwave background maps. The probability distribution (PDF) provides a powerful tool to test non-Gaussian features in the convergence field and to discriminate the different cosmological models. In this letter, we present a new PDF space Wiener filter approach to reconstruct the probability density function of the convergence from the noisy convergence field. We find that for parameters comparable to the CFHT legacy survey, the averaged PDF of the convergence in a 3 degree field can be reconstructed with an uncertainty of about 10%, even though the pointwise PDF is noise dominated.