The conflict in a story is a clash between two opposing forces, usually between the protagonist and the antagonist. Therefore, if we can identify the conflict of a story, we can also identify the protagonist and antagonist. While a conflict is often between two characters, a conflict can arise between many other forces in a story. Common conflicts, other than character vs. character, are character vs. society, character vs. nature, and character vs. self. Hence, in Ray Bradbury's short story "The Pedestrian," the antagonist does not necessarily need to be a character.
The protagonist of a story is the most easy to discern because the protagonist is the character the story centers around. It is also the character who undergoes change as a result of resolving the conflict. There is really only one central character in Bradbury's short story, and that character is named in the very first paragraph: Mr. Leonard Mead. As Bradbury describes, Mr. Mead is out for a walk at 8 pm on a November night in A.D. 2053, enjoying the silence of the night, something Mr. Mead "dearly loved to do."
To uncover the conflict, we have to figure out what Mr. Mead is battling against, which is very clearly revealed to us by the time Mr. Mead is pulled over by the city's one police officer. Through this conversation, we learn that Mr. Mead, though a writer, is considered as having no profession and that society thinks it completely unusual for any person to be out of doors "just walking" for absolutely no purpose. In his private thoughts, Mr. Mead explains to the reader exactly why his society finds him to be an outsider:
Everything went on in the tomblike houses at night now, he thought, continuing his fancy. The toms, ill-lit by television light, where the people sat like the dead, the gray or multicolored lights touching their faces, but never really touching them.
In other words, Mr. Mead prefers to be alive an out in the world, walking, whereas the rest of the people of his society prefer to be dead, staring blankly at televisions that dominate their minds.
While Mr. Mead is arrested and imprisoned by the police officer, it is not the police officer Mr. Mead is truly in conflict with--it is society. Members of society are oppressing Mr. Mead as well as themselves. Therefore, we can say that the antagonist of the story is society and the conflict is character vs. society.