Problem model

There's probably several ways to put the underlying problematic in a mathematical object. I, for one, tend to prefer the graph approach than the full probabilistic one.

Let's define the finite set of historical facts $ \mathcal{F} = \{f_{1},\dots,f_{n}\} $.
$ \forall i \in \{1,\dots,n\},

\begin{array}{lrcl}

  f: & \mathcal{F} & \longrightarrow & \{0,1\} \\
     & f_{i} & \stackrel{f}{\longmapsto} & f(f_{i}) = \left\{
                                                           \begin{array}{rl} 0 & \quad si\,f_{i}\,est\,arrivé \\ 
                                                                             1 & \quad si\,f_{i}\,est\,n'est\,pas\,arrivé
                                                           \end{array} 
                                                      \right

\end{array} $