This paper proposes a probabilistic energy and reserve co-dispatch (PERD) model to address the strong uncertainties in high-renewable power systems. The expected costs of potential renewable energy curtailment/load shedding are fully considered in this model, which avoids insufficient or excessive emergency control capacity to produce more economical reserve decisions than conventional chance-constrained dispatch methods. Furthermore, an analytical reformulation approach of PERD is proposed to make it tractable. We firstly develop an approximation technique with high precision to convert the integral terms in objective functions into analytical ones. Then, the calculation of probabilistic constraints is equivalently transformed into an unconstrained optimization problem by introducing value-at-risk (VaR) representation. Specifically, the VaR formulas can be computed by a computationally-cheap dichotomy search algorithm. Finally, the PERD model is transformed into a convex problem, which can be solved reliably and efficiently using off-the-shelf solvers. Case studies are performed on IEEE test systems and real provincial power grids in China to illustrate the scalability and efficiency of the proposed method.