Although word predictability is commonly considered an important factor in reading, sophisticated accounts of predictability in theories of reading are lacking. Computational models of reading traditionally use cloze norming as a proxy of word predictability, but what cloze norms precisely capture remains unclear. This study investigates whether large language models (LLMs) can fill this gap. Contextual predictions are implemented via a novel parallel-graded mechanism, where all predicted words at a given position are pre-activated as a function of contextual certainty, which varies dynamically as text processing unfolds. Through reading simulations with OB1-reader, a cognitive model of word recognition and eye-movement control in reading, we compare the model's fit to eye-movement data when using predictability values derived from a cloze task against those derived from LLMs (GPT-2 and LLaMA). Root Mean Square Error between simulated and human eye movements indicates that LLM predictability provides a better fit than cloze. This is the first study to use LLMs to augment a cognitive model of reading with higher-order language processing while proposing a mechanism on the interplay between word predictability and eye movements.