Three of a kind (three cards of matching face value, such as three 7's) does not beat a straight (five cards of any suit in sequential order) in poker. A straight hand will supersede a three of a kind in any potential scenario.
The hands that do beat a straight in poker are as follows: a flush, a straight flush, a royal flush and five of a kind (if playing with wild cards). The ranking of the hands in poker is based on the probability of receiving them, with more common hands having a lower ranking than less common hands. An exception to this is a variant of poker, sometimes known as "low-ball", in which the player with the lowest-ranking hand wins.