The number three has been used throughout history to represent many different things. As for how one justifies the use of the number three, the reader's knowledge weighs heavily upon the outcome of its assumed significance in a story.
Some common representations of the number three in history and literature: the triad or trinity (as seen in Christian theology); unity of mind, body and spirit; completeness (three is the smallest number of sides an object must have to be solid); mysticism and fairy-tales (granting of three wishes or the three little pigs); and life (past, present and future).
Therefore, in regards to Marquez's "A Very Old Man with Enormous Wings," one could justify the significance of the number three as a typical reference to Christian theology. The Old Man has been interpreted by some readers as an angel.
Another possibility, given the lack of directness by the author about the Old Man, can be linked to the story's existence as a text of "magic realism." Therefore, the text could use the number three as a representation of mysticism.