It is speculated that higher penetration of inverterbased distributed energy resources (DERs) can increase the risk of cascading tripping events due to voltage fluctuations. Quantifying this risk requires solving the dynamic state transition equations of tripping events for interconnected DERs. However, these equations lead to a complex non-equilibrium system, which does not settle into stationary steady state conditions due to the volatility of DERs/loads. Thus, tripping dynamic equations do not have an asymptotic solution, which implies that the non-equilibrium dynamic model cannot be used as a tractable basis for DER curtailment prediction and mitigation. To address this challenge, we apply a probabilistic approach, which employs Chebyshev's inequality to obtain an alternative timeinvariant dynamic state transition model for quantifying the risk of tripping for networked DERs. Unlike the original nonequilibrium system, the proposed probabilistic dynamic model is stationary, which enables operators to estimate the expected DER curtailment events asymptotically using DER/load statistics. Furthermore, by integrating this probabilistic state transition model into an optimization framework, countermeasures are designed to mitigate cascading tripping events. Since the proposed model is parameterized using only the statistical characteristics of nodal active/reactive powers, it is especially beneficial for practical systems, which usually are not fully observable in realtime. Numerical experiments have been performed employing real data and feeder models to verify the performance of the proposed technique.