I think they use interest rate futures contracts to come up with that number. This is a guess based on my experience with options trading, but there is a quantity called "delta" that measures how much the contract moves in relation to the underlying price.
When delta is very high, close to 1.00, then it means that for every point the underlying price moves, the contract moves the same amount. This happens when the contract is deep "in the money" like a contract for April rates at 4.50% when actual rates now are at 5.25%. When a contract is way "out of the money" the price hardly moves at all in relation to the underlying number, so the delta is near zero.
Delta can be interpreted as the probability that a contract will close in the money. That's why one that's in the money has a high delta, and one that's out of the money has a low delta. A contract that's right at the money would have a delta of 50%
So.... how do they figure out what the market thinks about rate increases? Right now rates are at 5.25%. So we look at the April contracts with a strike price of 5.50%, representing a 25 bps raise. If the delta on these contracts is 40%, we say that the market is pricing in a 40% probability of a 25 bps rate hike. Then we look at the contracts with a strike of 5.75% just for chuckles. These are way out of the money and only have a delta of 15% let's say. So the market is pricing in a 15% probability of a 50 bps rate hike.
The calculation for delta is part of a larger equation known as the Black-Scholes Option Pricing Model. And there's no way I'm looking it up again anytime soon, LOL, so don't ask me what it is.
Hope this helps though.
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