The article in Koine Greek serves two purposes. First, it has a purely syntactic role where it occurs to check features. Examples are the article before prepositional phrases, the article before names and places, the article before infinitive verbs, and most of the time, the article before participles.
Consider Matt 2:13: μελλει γαρ ηρωδης ζητειν το παιδιον του απολεσαι αυτο, “Herod is about to be searching for the child, to kill it.” The article “του” a genitive, singular, neuter, provides information not available in the infinitive verb απολεσαι “to destroy.” Thus, the article “του” is required for the mechanics of syntax so that the reader knows that the infinitive used as a noun is used as a genitive, singular, neuter.
The second role of the article is to indicate known information verses unknown. Mental Space Discourse Theory indicates that any discourse has a base space containing relevant information for the text producer and the text consumer. The known information is that information common to both producer and consumer of the text. Often the known/unknown information appears to be definite/indefinite, old/new, specific/generic, deictic, types of participant reference, and anaphor.
The theory of known or recently mentioned provides answers why the article is used or absent. Consider Matthew 24:21 θλιψις μεγαλη “GREAT Tribulation.” This is the first mention so we can conclude that the concept of the GREAT tribulation was not widely known. Notice also that this GREAT tribulation is different than the tribulation in 24:9, as indicate because both lack an article.
As we get further into this text, we notice that Matthew 24:29 has the prepositional phrase with the article “μετα την θλιψιν.” This indicates that the tribulation in Matthew 25:29 is the same as Matthew 24:21.
Also Mark 11:13 has no article on the first appearance of συκην, “fig tree,” but has the article on the second and third mention at Mark 11:20, 11:21. Thus we have another example of the discourse use of a noun that was not previously known or mentioned but is later known further in the text.