What can you infer about why Italy's surrender gave hope to the people in the Annexe in Anne Frank: The Diary of a Young Girl?

The life in the Annexe was filled with so much in way of
uncertainty.  There were some fundamental and tension ridden beliefs that lived besides
one another in this setting.  On one hand, there was an overwhelming condition of
despair.  Living in the annexe was a flight from death, and everyone in the annexe
understood it.  At the same time, in order to counteract the condition of total fear and
despair, there seemed to be an equally intense yearning for hope, to take hope in almost
anything.  Seeing that those hiding in the Annexe have little or no power in the social
setting, there was a tendency to see anything that happened as in a larger context than
might actually be.  When news of Italy's surrender hits, there is an immediate hope that
the war is close to being over and their life of hiding is over with it.  It is this
painful condition of striving to find hope in anything, everything that could lead to a
potential end to such a condition that enables the people in the Annexe to react the way
they do.  This hope becomes one of the most defining elements in Holocaust Literature
such as The Diary of Anne Frank.  It compels people to believe,
which is the source of both great strength and simultaneously great
delusion.