What kind of role does a baron hold in your setting? Are they powerful to the point of being social equals to the king, or are they basically the lowest of nobility? Are there viscounts, counts, marquis, dukes, etc. above them? Are they even directly a vassal of the king? A baron could be a vassal of other higher nobility instead of directly the king. For example in France, the duke of Normandy would be the liege lord of all counts and barons in Normandy, and his liege lord would ofc be the king of France. All the nobles are technically under the king, but the baron's corruption would be the problem of whatever liege he is sworn to first. Have you seen GoT? Imagine the rulers of the so called kingdoms as dukes, or maybe grand dukes, and how they have many sworn vassal lords under them. The GoT nobility system is quite a bit simplified tbh, but you get the gist of what can be.
If a baron is the lowest of nobility, he might be insignificant to the point that i would question why the king would even keep such a close eye personally for his misdeeds. There can be a few hundred barons in a kingdom, depending on the size. Would most likely only get to have a small manor or castle with some land, a few villages, or a city maybe. There would then be knights as vassals of nobles and king below, given small fiefs, and also landlords, there can be tens of thousands of them.
So, is the king keeping a close eye on hundreds of nobles like the mentioned baron with spies everywhere in their retinues? If so, i'm pretty sure this would already be a known secret to many of the other nobles. Some would keep the spies even when knowing, feeding them only deliberate information and some sprinkles of weaknesses, some would even outright get rid of them, just a game of power and balance in between nobility really. King wouldn't be raising any problems over dead spies who shouldn't even exist. Everyone knows they exist, but no one would openly claim as such unless something outrageous happens.
Also, it wouldn't really be strange for most nobles to have corruption to various degrees. What matters is how outrageous and bold they get with their corruption really. I mean, just look at the level of corruption that can exist in modern governments, let alone medieval times with nobles ruling over their lands with basically full judicial authority. They would all know there is corruption, but to persecute a noble the king better have some serious crime on him, or he might also be stepping on the toes of many other nobles with similar levels of misdeeds. If the king gets rid of this noble and his lineage for what is seen as a small reason or bs, who says they won't be next? That's how what you would think of as a king of justice, can become lauded as a tyrant instead.
