OK, I'll come clean. I am a member of a Probus Club. Yes, it is for retired professional and business men. In the same town is a women's Probus Club. And, in some cases, there are mixed Probus Clubs.
Let me talk about the club I know.
It is not the Presidents Club. The Presidents Club was (it appears to have been disbanded) a club for men possessing power, people excercising power on a daily basis. My guess is that these men's behaviour is influenced by testosterone. People with power - particularly those with power in formal organisations - like other people to know of their power. Some of them may behave in ways not dissimilar to stags, stallions and lions maintaining their harems. At an event at the Dorchester Hotel, free from the environmental context which constrains their behaviour, they let themselves relax in the presence of attractive, alluring, young women and some take the opportunity to be competitive ...
In my Probus Club there are men - some in their eighties and nineties - who are still sharp and intelligent. They are articulate and capable and are pleased to be able to spend time with others who share backgrounds. They offer each other friendship and warmth. There is no competition. The continued welfare of members is a significant factor which occupies the club. It is quite possible that for some, club meetings allay the loneliness the characterises their lives.
The club, in an undemonstrative manner, offers companionship and concern and mental stimulation to men that society in general has ceased to consider of prime importance, and when they have died, continues to do so to their widows.