One of the critical components in industrial gas turbines (IGT) is the turbine blade. The design of turbine blades needs to consider multiple aspects like aerodynamic efficiency, durability, safety, and manufacturing, which make the design process sequential and iterative. The sequential nature of these iterations forces a long design cycle time, ranging from several months to years. Due to the reactionary nature of these iterations, little effort has been made to accumulate data in a manner that allows for deep exploration and understanding of the total design space. This is exemplified in the process of designing the individual components of the IGT, resulting in a potential unrealized efficiency. To overcome the aforementioned challenges, we demonstrate a probabilistic inverse design machine learning (PMI) framework to carry out an explicit inverse design. PMI calculates the design explicitly without excessive costly iteration and overcomes the challenges associated with ill-posed inverse problems. In this study, the framework will be demonstrated on inverse aerodynamic design of three-dimensional turbine blades.