High penetration of distributed generation (DG) is mainly constrained by voltage-related issues. Due to the uncertainties associated with type, size, and location of DGs, it is difficult to quantify their integration limits in distribution networks, i.e., hosting capacity (HC). To address this issue, this paper proposes a probabilistic-based framework to determine the maximum integration limits of DGs considering the voltage rise and voltage deviation constraints. Such framework requires the use of the HC model, which can be formulated as a nonlinear optimization problem. Adding the voltage deviation constraint in the HC problem makes the model unsolvable. We address this issue by proposing a two-step algorithm to linearize the HC model. Then, using the linearized model, a probabilistic framework is proposed for considering the load variability and DGs uncertainties. To validate the efficacy and accuracy of the proposed framework, we identify the HC of a balanced and an unbalanced distribution networks and compare our results with those obtained from comprehensive power flow method and the traditional conservative planning. Finally, using the proposed framework, the impact of voltage deviation constraint, load growth, DG type and network structure on the HC are comprehensively studied using different DG technologies (i.e., Photovoltaics and wind).