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Probing is a popular method to discern what linguistic information is contained in the representations of pre-trained language models. However, the mechanism of selecting the probe model has recently been subject to intense debate, as it is not clear if the probes are merely extracting information or modeling the linguistic property themselves. To address this challenge, this paper introduces a novel model-free approach to probing, by formulating probing as a prompting task. We conduct experiments on five probing tasks and show that our approach is comparable or better at extracting information than diagnostic probes while learning much less on its own. We further combine the probing via prompting approach with attention head pruning to analyze where the model stores the linguistic information in its architecture. We then examine the usefulness of a specific linguistic property for pre-training by removing the heads that are essential to that property and evaluating the resulting model's performance on language modeling.