Like @Cookielnk is saying this very subjective and it largely controlled by the gameplay.
You need to carefully consider what feeling you want to provoke in players, a great analogue would be comparing two game genre such as racing games and horror games, in racing games you typically don’t rely as much on reaction but more so on who has the concentration to make least amount of mistakes during the race, while there certainly are racing games that combine the two. In horror games you almost always depend on reaction and quick wits making quick decisions to survive.
A suggestion would be, walk, run and sprint, sprint would typically be tied to breath AKA exhaustion.
Walk is typically slow, but will affect greatly how quickly you regain your breath, while running you typically regain breath much slower, both of which are also tied to if you fully exhaust your breath or not, fully exhaust may penalize players short term as it could for instance force player to walk for x amount of time before they can run again or have to wait for breath to reach a certain threshold before they can use sprint, some games if you fully exhaust breath, you have to catch your breath 100% before you can sprint again, if you fully exhausted your breath. There a large array of options to chose from having these two factors alone that can provoke very different feelings how encounters feel like, as an example these could also be tied to a skill system.
Running speed is the baseline of your calculation as this would be the easiest part to figure out.
As for speeds walking would be roughly somewhere between half to a third of what running would be, and sprinting a fourth to a third faster than what running would be.
Map layout is a important factor when you consider the run speed of monsters, in a open environment you would want monsters to run faster than players as players would then have to rely on sprint and obstacles to avoid getting caught.
In a closed environment such as mazes speed plays less of a factor as players would have to use their wits to avoid getting caught.
Sight is also something you should think of, in the horror genre in particular, most common you have limited sight and monsters can easily catch you off guard. While in racing you typically have much greater view of your surroundings to plan your next move, again just to convey the large difference in what each genre feels like.