Large language models (LLMs) have progressed rapidly in complex reasoning and question answering, yet LLM hallucination remains a central bottleneck that hinders practical deployment, especially for commercial black-box LLMs accessible only via APIs.Existing uncertainty quantification methods typically depend on computationally expensive multiple sampling or internal parameters, which prevents real-time estimation and fails to capture information implicit in the blackbox reasoning process.To address this issue, we propose Distribution-Aligned Adversarial Distillation (DisAAD), which introduces a generation-discrimination architecture to guide a lightweight proxy model to learn the highquality regions of the output distribution of the black-box LLM, thus effectively endowing it with the ability to "know whether the blackbox LLM knows or not".Subsequently, we use the proxy model to reproduce the specific responses of the black-box LLM and estimate the corresponding uncertainty based on evidence learning.Extensive experiments have verified the effectiveness and promise of our proposed method, indicating that a proxy model even one that only accounts for 1% of the target LLM's size can achieve reliable uncertainty quantification.Our model and related resources are released at https://github.com/huizi-Cui/ DisAAD.