Final answer:
The conflict in the poem involves the Mudville nine who are behind in the score with only one inning left to play, putting their hope in a player named Casey to win the game.
Step-by-step explanation:
The conflict in the poem is the challenging situation faced by the Mudville nine, a baseball team that is behind in the score and has only one inning left to play. The hope of the fans rests on a player named Casey getting to bat, since they believe he has the ability to turn the game around. The stakes are high, tensions are mounting, and the atmosphere is thick with anticipation and despair. It's a classic setup of a team's last chance for victory resting on the shoulders of a single individual.