The reason the chain stops minting SBDs for rewards is because it thinks (according to its formula) that there are too many SBDs in the ecosystem compared to the market-cap of Steem in the ecosystem. Since converting reduces the number of SBDs it will generally move things closer to a condition where SBDs will be minted for rewards. (It's slightly complicated by the dynamics of the economy, though, since things might affect the Steem price).

The amount of Steem and SBDs in the ecosystem are parameters that the chain keeps track of, so there are a number of ways to get that info. One way is to go to Steemworld.org and look at the Market Info tab, you'll see "Current Supply" of Steem and SBDs there, those are the number of tokens that exist in the world. (Some of those Steem are powered up, so it combines the two blue regions from the "pie chart" representation in the original post).