list manipulation - How do I divide the columns of a matrix by the sum of its elements?

I am trying to create a transition matrix for a network. In order to do this, I need to sum down the column (the out degree), and then divide the column by the out degree in order to normalize it.

I am able to sum down the column. What I am unable to figure out how to do efficiently and easily is to divide the column by the sum.

L = {{0, 1, 0, 1, 0, 0, 0}, 
     {0, 0, 1, 1, 1, 0, 0}, 

     {0, 1, 0, 1, 0, 0, 0}, 
     {0, 0, 0, 0, 1, 0, 0}, 
     {1, 0, 0, 0, 0, 0, 0}, 
     {0, 0, 0, 0, 0, 0, 1}, 
     {0, 0, 0, 0, 0, 1, 0}};

Answer

If you need to do this with all columns, then:

Transpose[#/Total[#] & /@ Transpose[L]]