I was studying about the markov property in reinforcement learning, which is supposed to be one of the important assumptions of this field. In that it says, that while considering the probability of the future, we consider only the present state and actions and not that of the past. An important corollary that arises when we consider the probability of the present state given future state/action, the future state/action can't be ignored as it has valuable information in the computation of the present probability.
I do not understand this second statement. From the point of view of the future event, the present event seems to be the past for this future event. Then why are we considering this past event?
Let's focus on these two sentences individually. The Markov Property (which should apply in your problem, but in reality doesn't have to) says that the current state is all you need to look at to make your decision (e.g. a "screenshot" -aka observation- of the chess board is all you need to look at to make an optimal action). On the other hand, if you need to look at some old state (or observation) to understang something that is not implied in your current state, then the Markov property is not satisfied (e.g. you can't usually use a single frame of a videogame as a state, since you may be missing info regarding the velocity and acceleration of some moving objects. This is also why people use frame-stacking to "solve" video games using RL).
Now, regarding the future events which seems to be considered as past events: when the agent takes an action, it moves from one state to another. Remember that in RL you want to maximize the cumulative reward, that is the sum of all the rewards long-term. This also mean that you basically want to take action even sacrifying instantaneous "good" reward if this means obtaining better "future" (long-term) reward (e.g. sometimes you don't want to take the enemy queen if this allows the enemy to check-mate you in the next move). This is why in RL we try to estimate value-functions (state and/or action). State value-functions is a value assigned to a state which should represent how good is being in that state in a long-term perspective.
How is an agent supposed to know the future reward (aka calculate these value functions)? By exploring a lot of states and taking random actions (literally trial and error). Therefore, when an agent is in a certain "state1" and has to choose between taking action A and action B, he will NOT choose the one that has given him the best instantaneous reward, but the one which has made him get better rewards "long-term", that is the action with the bigger action-value, which will take into account not only the instantaneous rewards he gets from the transition from state1 to the next state, but also the value-function of that next state! Therefore, future events in that sentence may seem to be considered as past events because estimating the value function require that you have been in those "future states" a lot of times during past iterations!
Hope I've been helpful