Why "Not a directory" instead of "No such file or directory"?

Consider this scenario:

$ file a b c
a: empty
b: cannot open `b' (No such file or directory)
c: cannot open `c' (No such file or directory)

$ file b/c
b/c: cannot open `b/c' (No such file or directory)

$ file a/b
a/b: cannot open `a/b' (Not a directory)

Why Not a directory instead of No such file or directory? Reason for the question: the ` a/b' (Not a directory)` may suggest that a/b needs to be a directory. However, a/b` may be a file. --- UPD. It seems that a/b may _not_ be a file because a is a file. Hence, the question: why `cannot open a/b' (Not a directory)` instead of cannot open a' (Not a directory)``?