That it is a little different. There you are estimating a continuous parameter (which happens to be interpretable as a probability) and it makes sense to have a probability distribution over that.

But if you are talking about whether a single discrete events will happen or not, a single number (the probability) already fully captures the uncertainty about it.

There is a lot of missing information in their probability of binary events presented. Presumably they polled N forecasters and are presenting an x/N prediction. The fact that each forecaster is estimating in a continuous space and then binarizing their result means that a lot of information has been lost.

To look at an extreme example… were all the “yes” votes 95%+ certain and the “no” votes just under the line 49%? Or was it more like a bunch of no votes at 49% and a bunch of yes votes at 51%?

Binarizing forecasts necessarily discards information. Aggregating a bunch of binary predictions into a percentage does no recapture said information, unfortunately.