If your string of symbols constitutes a passage of English text, then you could just count the number of words it contains. But this is silly: it would give the sentence "The Sun will rise tomorrow" the same information value as he sentence "The world will end tomorrow" when the second is clearly much more significant than the first. Whether or not we find a message informative depends on whether it's news to us and what this news means to us.
importantly, information depends on the prior knowledge of the receiver. If we have no idea about the relative frequency of sun rise and world ending, then the two sentences has the same amount of information to the receiver.