I think it should be in his plan. Chaos is a ladder, and climbing is everything. Chaos is a ladder, and only climbing is the whole of life. This sentence is the wisdom of Littlefinger. Throughout the play, you will find that Littlefinger is a radical person. This is not to say that he doesn't love peace, but that in a hierarchical aristocratic society, he only has a chance to win the upper position in chaos. As a parliamentary finance minister for many years, without knowing the nature of Joe the Great, he could not be good at calculation. From the time he plotted against Ned, he planned to kill Ned, because it would be easy to provoke a war between the northern border and King's Landing, so as to gain the benefits he wanted from the chaos of this war. What benefits? One is to kill Ned Stark, because they regard each other as rivals in love. Ned looks down on Littlefinger and looks down on him everywhere, which makes Littlefinger hate for a long time. The other can be seen from the later plot trend analysis that he wanted to destroy the Stark family with the help of Lannister, give himself a chance to seize the northern territory and rewrite his humble family bloodline. The above only represents personal views, I hope I can help you ~