If you have {publicly competent, publicly incompetent, privately incompetent, privately competent}, we get some information that screens off publicly competent. That leaves the narrower set {publicly incompetent, privately incompetent, privately competent}. So it’s still an update. I agree that in this case there is some room for doubt though. Depending on which institutions we are thinking of (Democratic party, newspapers, etc.), we also get some information from the speed at which people decided on/learned that Biden was going to step down.
If you have {publicly competent, publicly incompetent, privately incompetent, privately competent}, we get some information that screens off publicly competent. That leaves the narrower set {publicly incompetent, privately incompetent, privately competent}. So it’s still an update. I agree that in this case there is some room for doubt though. Depending on which institutions we are thinking of (Democratic party, newspapers, etc.), we also get some information from the speed at which people decided on/learned that Biden was going to step down.