What is a weighted or probabilistic automaton?
The setting you suggest is not clear enough to determine what kind of an automaton you are looking for.

A short explanation regarding the types of automata:

A weighted automaton is typically an automaton with a weight function on the edges (or states). Then, a run is assigned a weight according to the weight it traverses. There are many different semantics for the value of a run. These include the maximum/minimum weight, the sum, a discounted sum, an average, etc. Finally, nondeterminism is resolved with some semantics. Typically max/min.

The important thing is that a weighted automaton defines a function $f:\Sigma^*\to \mathbb{R}$, instead of a Boolean language (which can be thought of as a function $g:\Sigma^*\to \{0,1\}$).

Probabilistic automata can be thought of as a sort of weighted automata, but a distinction is usually made (mainly because weighted automata are often defined over a tropical semi-ring). In probabilistic automata, the "weights" (probabilities) are multiplied along a run, and the sum of the (accepting) runs is taken. 

If you elaborate or demonstrate the scenario you are thinking of, perhaps I can modify the answer to suggest an appropriate model.