In distribution networks, different methods are used to reduce power loss, improve voltage profile, and release the capacity of lines. Among them, methods related to capacitor placement and conductor selection have common objectives and can result in significant improvements in distribution networks if implemented simultaneously. By using these methods, in addition to achieving the abovementioned objectives, the load supply capability of distribution networks, which indicates the amount of allowable increase in load, can also be improved. In this study, optimisation algorithms are implemented to solve optimal capacitor placement and conductor selection in a radial distribution network including renewable power generations. These algorithms consider different goals such as improving load supply capability. Furthermore, due to the existence of uncertainties such as load variations and fluctuations in output power, a probabilistic evaluation needs to be performed on the distribution network. To do so, the probabilistic and efficient approach of spherical unscented transformation is used. The most important feature of this approach is that it takes the correlation between the random input variables of the problem into consideration. The results of this probabilistic evaluation are used for conductor selection and capacitor placement by means of a radial 30-bus distribution network.