Transiting planet surveys provide a great deal of data for studying the exoplanet compositions via the relationship between masses and radii (M-R relation). However, usually only one of the mass or radius measurement is available for newly discovered planets, which makes it necessary to estimate M-R relation conditioned on a sample of planets with both masses and radii measured but subject to measurement errors. Majority of the statistical models available in the literature on probabilistic M-R relation assume that the planetary masses are normally distributed around the means determined by the power law without any justification. Given the power law relation, using the well known Maximum Entropy Principle, we shown that the conditional distribution of masses (given radii) follows an exponential distribution where the conditional mean is modeled using a flexible multiple knot-based power law structure. Parameter estimation is carried out using Bayesian methods that not only account for measurement errors but also perform proper imputation using posterior predictive distributions. Two data sets are used to illustrate the flexibility and broad applicability of the proposed model.