Heisenberg’s uncertainty relation is derived here from Nelson’s stochastic quantization procedure introducing Brownian motion in the internal space of a particle apart from that in the external space. This helps us to have a relativistic generalisation of Nelson’s formalism when a relativistic quantum particle appears to be a stochastically extended one. The nonrelativistic formalism is obtained in the sharp point limit. Quantum probability is found to be a manifestation of the internal geometry in this sharp point limit.