Uncertainty quantification (UQ) methods for Large Language Models (LLMs) encompasses a variety of approaches, with two major types being particularly prominent: information-based, which focus on model confidence expressed as token probabilities, and consistency-based, which assess the semantic relationship between multiple outputs generated using repeated sampling. Several recent methods have combined these two approaches and shown impressive performance in various applications. However, they sometimes fail to outperform much simpler baseline methods. Our investigation reveals distinctive characteristics of LLMs as probabilistic models, which help to explain why these UQ methods underperform in certain tasks. Based on these findings, we propose a new way of synthesizing model confidence and output consistency that leads to a family of efficient and robust UQ methods. We evaluate our approach across a variety of tasks such as question answering, abstractive summarization, and machine translation, demonstrating sizable improvements over state-of-the-art UQ approaches.