Aggregators are expected to become an inevitable entity in future power system operation, playing a key role in unlocking flexibility at the edge of the grid. One of the main barriers to aggregators entering the market is the lack of appropriate models for the price elasticity of flexible demand, which can properly address time dependent uncertainty as well as non-linear and stochastic behavior of end-users in response to time varying prices. In this paper, we develop a probabilistic price elasticity model utilizing quantile regression and B-splines with penalties. The proposed model is tested using data from residential and industrial customers by assuming automation through energy management systems. Additionally, we show an application of the proposed method in quantifying the number of consumers needed to achieve a certain amount of flexibility through a set of simulation studies.