'Public' in the Bible

Now in Jerusalem near the sheep-market there is a public bath which in Hebrew is named Beth-zatha. It has five doorways.

For no one does anything in secret while he’s seeking public recognition. If You do these things, show Yourself to the world.”

And look, he is speaking in public, and they are not saying anything to him! Can it be that the authorities really know that this is the Messiah?