Unobtrusive sensor-based recognition of Activities of Daily Living (ADLs) in smart homes by processing data collected from IoT sensing devices supports applications such as healthcare, safety, and energy management. Recent zero-shot methods based on Large Language Models (LLMs) have the advantage of removing the reliance on labeled ADL sensor data. However, existing approaches rely on time-based segmentation, which is poorly aligned with the contextual reasoning capabilities of LLMs. Moreover, existing approaches lack methods for estimating prediction confidence. This paper proposes to improve zero-shot ADL recognition with event-based segmentation and a novel method for estimating prediction confidence. Our experimental evaluation shows that event-based segmentation consistently outperforms time-based LLM approaches on complex, realistic datasets and surpasses supervised data-driven methods, even with relatively small LLMs (e.g., Gemma 3 27B). The proposed confidence measure effectively distinguishes correct from incorrect predictions.