Large language models (LLMs) have been widely employed across various application domains, yet their black-box nature poses significant challenges to understanding how these models process input data internally to make predictions. In this paper, we introduce a precise and quantitative law that governs the learning of contextualized token embeddings through intermediate layers in pre-trained LLMs for next-token prediction. Our findings reveal that each layer contributes equally to enhancing prediction accuracy, from the lowest to the highest layer -- a universal phenomenon observed across a diverse array of open-source LLMs, irrespective of their architectures or pre-training data. We demonstrate that this law offers new perspectives and actionable insights to inform and guide practices in LLM development and applications, including model scaling, pre-training tasks, and interpretation.