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.