How math maps real world problems

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Please remember that I'm not a math or science student - quite a layman in these areas. Therefore, please explain your reply in as much detail as possible. Thank you.


I found the attached (modified) image on this webpage:
http://gravityandlevity.wordpress.com/2009/04/01/entropy-and-gambling/

According to the the graph probability for getting a value between 'green' and 'red' dots is zero. Perhaps, it's true in mathematical terms. But I don't think in 'real' world getting a value between 'green' and 'red' dots is impossible. I'm curious to know how math maps real world problems. Please help me.
 

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The graph is an approximate representation of the numbers. The probabilities between the green and red dots are not zero. However they are so small they can't be displayed on the graph.
 

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