Hi

I will start with describing the problem and then ask my question

Assume you have two state spaces (State A, State B)

State A is depending on two variables (alpha and beta)

the range of variables values are

for alpha : [-100,100]

for beta : [-50,50]

State B is depending on three variables (distance, gama and alpha)

the range of variables values are

for alpha : [-50,50]

for gama : [-40,40]

distance : [0,300]

State A will give me a unique number, denoted by s1, calculated from the values of the space variables (alpha and beta).

State B will give me a unique number, denoted by s2, calculated from the values of the space variables (distance, gama and alpha).

MY QUESTION IS

is it possible to find the probability of the similarity between State A and State B by using the conditional probability of the two state spaces. Note that the two state spaces are sharing one state variable (alpha)

such as Pr(A) = Pr(A|B) where Pr is the conditional probability.

if this is not possible, do you have any other idea to check the similarity between two different state space.

with best wishes