You get a certain amount of Experience Points for a certain level of difficulty. For instance, solving an easy mystery will always earn you 20 experience.
Experience points, in turn, earn you skill points. However, there is a law of diminishing returns. The more experience points you have, the more you need to earn additional skill points. So, while a new detective gets one skill point for every 10 experience points, a detective that's been around a while (has a lot of experience), might only receive one skill point for every 20 or 40 experience.
In the case of "a", you solved some really hard mysteries right off the bat, meaning you earned a lot of experience all at once. And, since it was a brand new detective, you got a lot of skill points with that experience.
You'll notice I added a couple of controls to limit the ability of detectives to advance that quickly. The big ones are that you now can't take on really hard cases until you have some experience. This is to force people to work up the ladder a little more realistically.