It has been shown that when humans require a brief moment of concentration or mental effort, they tend to avert their gaze away from the attended location (or even blink). Similarly, participants tend to miss unexpected events when they are highly focused on a task. We present an engagement theory of distractibility that is meant to capture the relationship between participants’ engagement in a task and reduction in sensitivity to new sensory events in a broad range of situations. In a series of experiments, we asked participants to perform different cognitive tasks of varying degrees of difficulty while we measured spontaneous oculomotor capture by new images that were completely unrelated to the participants’ task. The images appeared while participants were cognitively engaged in the task. Our results showed that increased cognitive engagement produced decreased sensitivity to visual events. We propose that individual differences in intrinsic motivation play a large role in determining sensitivity to task unrelated events. In addition, our results also indicate that changes in task difficulty on a trial-to-trial basis do not generate trial-by-trial differences in oculomotor capture. Importantly, we believe our framework provides us with a promising way of extending laboratory findings to many real world situations.