@jokerxhisoka 'cept the king himself confirmed that he wasn't there. We also know the time table isn't that huge on this, it's not like she's been gone a year. So everything I said pretty much automatically becomes true, unless something that the manga hasn't shown us exist. And saying that is the case is the assumption.
You're assuming there is some way for the King to have found out that his daughter ran away, or that the MC at least knows of a way and should thus be suspicious of the king. Because no matter how you look at it, the manga -confirms- that the king wasn't there and was unaware of what happened. He even said "What did you plan on doing to your sister" and the guards tried to explain "What the big sister did to teh little sister" if the king was there for it, they wouldn't need to explain. This is some basic reading comprehension stuff. There is no reason for the MC to doubt the fact that the king was unaware of what was happening, and thus no reason to be suspicious of the king not sending people after his older daughter.
Edit: Now if you're talking about his lack of caution with following the king, that's something different, but also kinda a bad call, cause he is cautious, but also way stronger than them. Remember, he can see stats. So even if the King plans on trying to back stab him, he's confident he can get out of it with his stats and abilities.