Calculating probability of next event given remaining count and range for each (Apologies if my use of terms is off - I am not a mathematician by trade and what I did learn way back was in a different language)
What I know:
the total length of the stream, the body of possible events, the pop-count for each event, and the range of each event (essentially the index of the last instance of this event).
What I want:
Given an incoming stream of events I am trying to predict what the next event is likely to be, i.e. calculate the probability of the next event being a particular one of the known population.
Example:
Let's say the incoming stream is
ABABCCCC (not known by the receiver)

Known by the receiver:
Length=8

   Count Range 
2     3     0.25
B: 2     4     0.25
C: 4     8     0.50

When looking at the range we can calculate the local probability of each event being next (by local I mean considering only the current event).
   Count Range Local prob