In which team sport does a match have the highest probability of the winner being decided in the final minute?

The intent of the question undoubtedly is which team sport has the highest probability of the team that was behind with a minute left overcoming that deficit and winning. Also the 1600 meter relay race is an event that is part of a larger sport.

The sport should have certain characteristics. The event is generally close, contributing to the probability that changes in the lead may occur. The lead in the event can change rapidly, due to the ease of scoring points or changes in speed.

I would say (opinion only) that basketball fits this best, although I wouldn't discount rowing.

I would have thought that scoring was such a common event in basketball that scores are not so likely to be that close within a minute of the end. Races like the 1600 metres relay and rowing don't really feature a "match" as mentioned in the question.

The question is really speculative, and an interesting debate topic, but not one which has a factual answer. Even if it were defined more precisely so as to apply to team sports with progressive scoring, and maybe including untimed games (since a baseball game, for example, could be won by a hit off the final ball of the game either in the ninth inning or in extra innings), and requiring that the winning team had been trailing at the start of the last minute, still there is no valid basis for determining probability. One could make an estimate, if enough records were available, by determining for each sport the percentage of games that have been won in the last minute, and ranking them. This would produce a rough predictive probability, but it would have a large margin of error. And take an amazing amount of data collection!