It all depends on the terms of the scheme, IMO - this is obviously an occupational pension and the terms may vary. It is correct that the man's pension stops when he dies, then any widow's entitlement will start. I don't understand the probate part but that's my ignorance of the arrangements, not that I mean that it's wrong.
The widow's pension being discretionary doesn't mean they could stop it once started, IMO - it means that it's not a right to grant it in the first place, and under certain circumstances the Trustees might agree not to pay it (but again the pension terms need to be seen, not guessed at).