<p>The transmission grid is a pivotal part of any power system that needs significant expansion costs to supply increasing electric loads reliably. The transmission network expansion planning (TNEP) that aims to identify the best expansion plan is a complex problem with deep uncertainty. The tri-level robust optimization (RO) model has been extensively employed to deal with uncertainty in the TNEP problem, aiming to obtain a robust, least costly solution against the possible uncertainty realization. The current RO-based TNEP models consider a specific interval for each uncertain parameter without assigning any probability to that interval's lower and upper limits. However, a probability can be assigned to these lower and upper values. This implies that the possible realization of any uncertain parameter at the vertices can have a particular probability. This article aims to present an RO framework for the TNEP problem where, unlike the existing approaches, some specific values as probabilities are linked to the lower and upper limits. In this regard, several constraints are constructed and added to the second level so that the probability of the chosen worst-case uncertainty realization is above a desired predetermined amount. The multiplications of many binary variables are successively linearized to acquire a linear model. The column-and-constraint generation (CCG) technique solves the formulated model. Results signify the applicability and scalability of the established scheme.</p>