As power systems transition toward high renewable penetration, assessing stability through deterministic margins is becoming obsolete due to rising operational uncertainties. This paper develops a novel probabilistic risk‐based framework to compute a Global Instability Index, which simultaneously accounts for rotor angle, voltage, and frequency stability under large‐scale disturbances. The primary goal of this research is to establish a rigorous and risk‐based global instability framework capable of simultaneously assessing distinct stability modes in modern and converter‐heavy networks. Using the IEEE 39‐bus test system, the study systematically evaluates the impact of increasing wind power penetration from 20% to 80%. Quantitative analysis reveals that the integration of doubly fed induction generator (DFIG)–based wind farms provides a stabilizing effect, lowering the global instability risk by approximately 46.8% at maximum penetration levels. Detailed case studies investigate the influence of shifting generation patterns and load fluctuations, demonstrating that the proposed global index serves as a more robust indicator of system health than conventional single‐variable metrics. These findings suggest that modern wind generation, when properly integrated, can effectively mitigate the risks associated with traditional synchronous machine displacement.