I was hoping keychain would share passwords between Macs

I have a Mac Pro, Macbook Pro and Macbook Air.

I hoped that having my Keychain available on iCloud would mean I could use my Skype account on any of them.

It has not worked.

Not only can I not log onto Skype using my hitherto unused-on-Skype Macbook Pro, I can no longer manually look up the password on my Air as I could before.

If I open Keychain on the Air and tick on the show password box nothing happens and the box remains un-ticked. If I look on the iCloud keychain on the new Macbook Pro, it asks for the keychain password but still doesn't display the password.

So now I can't remember the password and can't get it in the old way.

Anybody know why not?