All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the word at serial number $n$ be denoted by ${{\rm{W}}_{\rm{n}}}$. Let the probability ${\rm{P}}\left( {{{\rm{W}}_{\rm{n}}}} \right)$ of choosing the word ${{\rm{W}}_{\rm{n}}}$ satisfy ${\rm{P}}\left( {{{\rm{W}}_{\rm{n}}}} \right) = 2{\rm{P}}\left( {{{\rm{W}}_{{\rm{n}} - 1}}} \right),{\rm{n}} > 1$.
If ${\rm{P}}({\rm{CDBEA}}) = \frac{{{2^\alpha }}}{{{2^\beta } - 1}},\alpha ,\beta \in \mathbb{N}$, then $\alpha + \beta $ is equal to : ______