The plastic deformation of metallic glasses (MG) is well-known to occur via shear transformation zones (STZs) on the scale of atomic clusters, yet fracture of MG takes place via shear bands of the micron scale. So far, understanding on how the operation of STZs leads to shear localization and fracture remains limited. In this work, tensile tests on Cu/Zr-based MG micro-wires show that both the first-yield and fracture stress exhibit the Weibull distribution, and fractography reveals that shear localization in the form of intense shear bands leads to shear fracture. Molecular dynamics (MD) simulations show that shear bands form via the correlated emergence and operation of discrete STZs close to one another. To describe how the stochastic yet correlated occurrence of the discrete STZs leads to shear localization, a model is constructed to relate the probability of the successive operation of discrete STZs, to their nucleation density. The model predicts that, if nucleation density of the STZs grows along the strain path, as prior shear events triggers the emergence of new STZs, then successive occurrence of discrete shear events speeds up rapidly to an asymptotic state which is exactly the condition of shear localization and shear banding. Furthermore, the MD results suggest an exponential growth law for the occurrence of the STZs along the strain path, which also gives predictions in good agreement with the experimental Weibull distributions of the first-yield stress of Cu/Zr-based MGs.