We have developed a probabilistic fracture mechanics (PFM) analysis code named PASCAL4 for evaluating the failure frequency of reactor pressure vessels (RPVs) through consideration of neutron irradiation embrittlement and transients such as pressurized thermal shock events. It is well-known that flaw distributions, including flaw size and density, have an important role in the failure frequency calculations of a PFM analysis. NUREG-2163 report provides a methodology to obtain much more realistic flaw distributions based on a Bayesian updating approach by reflecting the non-destructive inspection (NDI) results, which is applicable for case when there are flaw indications through NDI. There may, however, be no flaw indications resulting after inspection of some RPVs. Therefore, we proposed likelihood functions applicable for both cases when flaws are detected and when there is no flaw indication as the NDI results. In the Bayesian updating method, the likelihood functions were applied to independently acquire the posterior distributions of flaw depth and density using the same NDI results. In this study, we further improve the likelihood functions to enable them to update flaw depth and density simultaneously. Based on this improved likelihood function, several application examples are presented where the flaw distributions are estimated by reflecting the NDI results through Bayesian update. In addition, PFM analyses are also performed considering those estimated flaw distributions. All the results indicate that the improved likelihood functions are useful for estimating flaw distributions.