When you buy new Converse shoes, the soles may not be non-slip because they haven't touched the ground yet.
To make them non-slip, walk on hard ground like concrete or gravel or use sandpaper to rub the soles for a few minutes. Coarse 15-grit sandpaper is best, but you can also use fine sandpaper or a nail file.
If you don't have access to hard ground or sandpaper, try using hair spray or puff paint to add a thin layer to the soles and let it dry.
However, these methods may not be as effective as commercial products like grip pads or tacky spray, which you can buy for about $10.