Legged robots have shown remarkable progress in walking over challenging terrain. However, they remain vulnerable to critical hardware failures due to unexpected accidents. In this paper, we introduce a framework that enables rapid adaptation to unexpected configuration changes in legged robots. To achieve this objective, we leverage a latent space to generate reusable prior knowledge by mapping capable walking trajectories (i.e., sequences of joint positions). This learned prior guides exploration in new leg configurations, enabling rapid adaptation to unexpected changes with efficient locomotion trajectories. We validate our framework by assessing whether previously learned walking strategies can be effectively applied to new configurations using a modular robot designed to operate in various leg configurations. Our results show that the proposed method outperforms baseline approaches in terms of rapid adaptation across different leg configurations ranging from six to three legs in both simulation and real-world environments.