Information and Black Swans

Shannon defined information received in a message as the logarithm of the inverse probabilty of the message. If the Sun comes tomorrow, the probability of that event is close to one, the inverse probability is also close to one, so the information received is close to zero.
A Black Swan has a low probabilty of occurrence , almost zero; so the inverse of that number is close to infinity and likewise with the logarithm. These low probabilty events could have a big impact, like the the collapse of the World Trade Building on September 11, 2001.

Shannon's definition does not incorporate the consequences of the event happening, he worked for the American Telephone and Telegraph company, his bosses did not care about the consequences of the message, only with the faithfullness with which their system would deliver the message, any message.

One could define a new measurement of probability that takes into account consquences, in this measure, Black Swans are heavy.