Do non-competitive inhibitors push out enzymes?

I understand how competitive inhibitors slow reaction rate by competing with the enzyme for the active site; but for non-competitive inhibitors, how do they *shut down* the reaction rate? Wouldn't some of the enzymes be able to get to the active site before the inhibitors changed the shape of them all in the same way that some enzymes are able to beat competitive inhibitors to the active site? Or are non-competitive inhibitors able to bond with the substrate and push out enzymes that have already bonded to the active site?