The answer to this question can be found towards the end of the book, after Montag has managed to successfully flee the Mechanical Hound and finds his way onto the train track that leads out of the city and towards freedom and an uncertain future. However, as he begins to walk away, he is filled with a sudden certain feeling about something that he feels is incontrovertibly true, even though he has no tangible proof to support his feeling. Note how this belief is expressed:
Once, long ago, Clarisse had walked here, where he was walking now.
This certain feeling reflects potentially two things. Firstly, that Clarisse, like him, managed to escape the city and make her way towards freedom. Secondly, it could also mean that Clarisse metaphorically walked the same path as Montag did in rejecting the totalitarian control of the society that is obsessed with providing fake "families" for its citizens and destroying anything that might upset the power that they have over their populace. In this sense, Montag is only walking the same path as Clarisse did as she rejected dystopian control and lived her own independent life.