Answer:
To avoid negative perception of the government. They needed someone to blame in order to save themselves and seem in charge.
Step-by-step explanation:
In Part Three, Montag manages to escape from the authorities and goes on a journey down the river to the wilderness. He meets a group of intelligent travelers there. After Granger and the smart people become friends with Montag, Granger switches on a small TV, which is still showing the police chase. Even though Montag has run away and is safe in the wild, the people in charge keep following and blaming an innocent person instead of admitting they failed. Granger tells Montag that the authorities want a quick and satisfying conclusion to make the audience happy and avoid embarrassment. That's why they start chasing an innocent person. Montag sees the Mechanical Hound go after an innocent person to stop the police chase. Basically, the people in charge choose to catch an innocent person as a way to divert blame and please the crowd, who only cares about appearances. The people in charge know that if they announce that Montag escaped successfully, it will make them feel embarrassed and might make other people who disagree with them want to challenge their power.
I hope this helps ! <(￣︶￣)>