Restore record profile button state to initial when profile being recorded is deleted

Profile being recorded property is reset to null only after notifying all listeners so that they can check if current profile is removed.

BUG=338311
R=alph@chromium.org

Review URL: https://codereview.chromium.org/148373002

git-svn-id: svn://svn.chromium.org/blink/trunk@165854 bbb929c8-8fbe-4397-9dbb-9b2b20218538