We propose that the underlying context of holographic duality and the Ryu-Takayanagi formula is that the volume measure of spacetime is a probability measure constrained by quantum dynamics. In anti-de Sitter JT gravity, we define and analyze the quantum stochastic process induced by the boundary, and show Einstein’s equations arise from the evolution of probability under the non-Markovian process. In particular, the area of compactified space in the gravitational theory can be identified as a probability distribution evolving under the quantum process. Extrapolating these and analogous results in flat JT gravity, we conjecture that general relativity arises in the semi-classical limit of the evolution of probability with respect to quantum stochastic processes.