I read the previous chapter and rakan's timing was perfect was because he anticipated the whole thing from much earlier on. He even mentioned the part that failed to jinshi before telling him to assign mao mao to solve the problem of the three brothers. In a manner of speaking, he was trying to save jinshi's life but like mao mao he couldn't do more than speculate
Edit - The old officer who died (sake/weed don't remember) would have noticed the irregularities much earlier on so he was taken out. The question is is elaborate plot to assassinate jinshi who is prob. the emperor's brother. The thing is rakan also say this in jinshi's persence that people who have talent should be in positions to utilize it.
I bet there is a war of succession being fomented (by the nobles), rakan backs jinshi while there are others (it could be the king himself) attempting to assassinate him