An example of irony in Montag's chase is that it becomes such a huge media event, while actually being of little significance. Helicopters fly over the city and a second Mechanical Hound is set loose to hunt Montag; the populace is entreated to find Montag, to turn him in or restrain him, and all the reports show him as a homicidal lunatic, of great danger to the city. In the middle of this, he overhears a radio report:
Through the aluminium wall he heard a radio voice saying, "War has been declared." The gas was being pumped outside. The men in the beetles were talking and the attendants were talking about the engines, the gas, the money owed.
(Bradbury, Fahrenheit 451, Google Books)
The war, which has been hinted throughout, has finally started; this is a war that will ultimately destroy the entire city. However, the people watching their televisions only see the danger of Montag, a single person who has read a book. The irony is that the government is so obsessed with controlling the news media and the popular opinion that the entirely ignore the impending war in favor of a sensationalistic story endangers no one, and is of no consequence when the bombs level the city.