Option 1 -> "Connection for" is not a standard English collocation and sounds unnatural.
Option 2 -> "Connection with" is the correct idiomatic expression used when indicating a relationship or link between two things or facts.
Option 3 -> "Connection behind" is grammatically incorrect and not used in standard English.
Option 4 -> "Connection to" can work in some contexts (physical connections), but "connection with" is the proper collocation when discussing relationships between facts or ideas.
Hence, Option 2: with -> The noun "connection" collocates with the preposition "with" when expressing a relationship or link between two facts, making "has no connection with" the correct phrase. -> correct