Background: Cone-beam computed tomography (CBCT) plays a crucial role in image-guided radiotherapy, but artifacts and noise make them unsuitable for accurate dose calculation. Artificial intelligence methods have shown promise in enhancing CBCT quality to produce synthetic CT (sCT) images. However, existing methods either produce images of suboptimal quality or incur excessive time costs, failing to satisfy clinical practice standards. Methods and materials: We propose a novel hybrid conditional latent diffusion model for efficient and accurate CBCT-to-CT synthesis, named HC$^3$L-Diff. We employ the Unified Feature Encoder (UFE) to compress images into a low-dimensional latent space, thereby optimizing computational efficiency. Beyond the use of CBCT images, we propose integrating its high-frequency knowledge as a hybrid condition to guide the diffusion model in generating sCT images with preserved structural details. This high-frequency information is captured using our designed High-Frequency Extractor (HFE). During inference, we utilize denoising diffusion implicit model to facilitate rapid sampling. We construct a new in-house prostate dataset with paired CBCT and CT to validate the effectiveness of our method. Result: Extensive experimental results demonstrate that our approach outperforms state-of-the-art methods in terms of sCT quality and generation efficiency. Moreover, our medical physicist conducts the dosimetric evaluations to validate the benefit of our method in practical dose calculation, achieving a remarkable 93.8% gamma passing rate with a 2%/2mm criterion, superior to other methods. Conclusion: The proposed HC$^3$L-Diff can efficiently achieve high-quality CBCT-to-CT synthesis in only over 2 mins per patient. Its promising performance in dose calculation shows great potential for enhancing real-world adaptive radiotherapy.