It seems that the vast majority of suits are not shatnez. If so is there a chiuv to have suits checked? If so, why? (Please provide sources).
The question is what type of suit goes into the calculation of the “majority.”
We cannot pool all suits together, because there might be a significant different between suits made in Poland and in England, Marks & Spencer suits, or suits that are 100% wool or those that are only 60% wool.
However, you are right that if for a particular type of suit there is a great majority of suits that are not Shatnez, there will no longer be an obligation to have the suit checked.
Because of the difficulty of grouping together suits for this purpose, and because of the fact that there is often a “significant minority” that have Shatnez, it is generally customary to have suits checked.
However, it is often permitted to wear an unchecked suit, where checking can’t be done, because of the presence of a majority.
Rav Moshe Feinstein (Iggros Moshe Yoreh De’ah 1:72), and other Poskim, have ruled that even where there is only a small minority of clothes with Shatnez, it is proper to have them checked.
For sources on this matter, please see the Sefer HaShatzen BeHalacha, p. 208ff.
It is possible that relying on the majority for clothing is more strained than in general, because the fact of the matter depends on people and not on nature.