This contribution seeks to provide a rational probabilistic explanation for the intelligibility of words in a genetically related language that is unknown to the reader, a phenomenon referred to as intercomprehension. In this research domain, linguistic distance, among other factors, was proved to correlate well with the mutual intelligibility of individual words. However, the role of context for the intelligibility of target words in sentences was subject to very few studies. To address this, we analyze data from web-based experiments in which Czech (CS) respondents were asked to translate highly predictable target words at the final position of Polish sentences. We compare correlations of target word intelligibility with data from 3-g language models (LMs) to their correlations with data obtained from context-aware LMs. More specifically, we evaluate two context-aware LM architectures: Long Short-Term Memory (LSTMs) that can, theoretically, take infinitely long-distance dependencies into account and Transformer-based LMs which can access the whole input sequence at the same time. We investigate how their use of context affects surprisal and its correlation with intelligibility.