Can a contingency table be used to model probabilities?

Its been a while since I did any serious statistics. I have been reading about contingency tables recently and it seems like they may offer a solution to my problem. There are people on here that know more about statistics than what I can ever expect to know, so rather than trying to "discover" things by myself, (and wasting time in the process), I decided to come here first, explain what I'm trying to do and ask the gurus here first, if it makes any sense, and second, if there is a better (and probably more simple/robust) way of achieving what I'm trying to do (highly likely I suspect).

Here is an overview of what I am trying to model:

I have a process which at any time, can be in one of N states. I have identified 4 other 'factors' that I believe are predictors of the state in which the system will be. The 'factors' are a mixture of categorical and real variables.

I am thinking of creating a multidimensional contingency table like this:

Factor1, # Dimension 1
Factor2, # Dimension 2
...
Factor4, State1  | State2  | State3  |  ... | StateN  |


where the value in a cell is the count of the number of times that the system has been in that state given the 'levels' of the four factors.

I am hoping to use this table then to build a probabilistic model (maybe using a suitable logistic function?) to be able to answer questions of the form:

What is the probability of the system changing from state i to state j, given Factor1, .. Factor4 are at a certain specified level?

Am I able to use a contingency table to do this?

Last but not the least, I don't know if contingency tables are part of non parametric statistics - but I hope there are no strong assumptions of normality of the variables etc. If there are any strong assumptions required for the use of a contingency table, I will be grateful if someone could alert me of the fact, and hopefully suggest another method that can allow me to model the probabilities in the manner I described above.

PS: If I have fudged up any of the terms in my question, please advise so I can edit my question to make it more clear. I know that the use of 'factors' and 'levels' in my question may be a tad confusing, but I could not think of any better labels.

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