Pandas sum across columns and divide each cell from that value

More simply:

result.div(result.sum(axis=1), axis=0)

Try the following:

In [1]: import pandas as pd

In [2]: df = pd.read_csv("test.csv")

In [3]: df
Out[3]: 
  id  value1  value2  value3
0  A       1       2       3
1  B       4       5       6
2  C       7       8       9

In [4]: df["sum"] = df.sum(axis=1)

In [5]: df
Out[5]: 
  id  value1  value2  value3  sum
0  A       1       2       3    6
1  B       4       5       6   15
2  C       7       8       9   24

In [6]: df_new = df.loc[:,"value1":"value3"].div(df["sum"], axis=0)

In [7]: df_new
Out[7]: 
     value1    value2  value3
0  0.166667  0.333333   0.500
1  0.266667  0.333333   0.400
2  0.291667  0.333333   0.375

Or you can do the following:

In [8]: df.loc[:,"value1":"value3"] = df.loc[:,"value1":"value3"].div(df["sum"], axis=0)

In [9]: df
Out[9]: 
  id    value1    value2  value3  sum
0  A  0.166667  0.333333   0.500    6
1  B  0.266667  0.333333   0.400   15
2  C  0.291667  0.333333   0.375   24

Or just straight up from the beginning:

In [10]: df = pd.read_csv("test.csv")

In [11]: df
Out[11]: 
  id  value1  value2  value3
0  A       1       2       3
1  B       4       5       6
2  C       7       8       9

In [12]: df.loc[:,"value1":"value3"] = df.loc[:,"value1":"value3"].div(df.sum(axis=1), axis=0)

In [13]: df
Out[13]: 
  id    value1    value2  value3
0  A  0.166667  0.333333   0.500
1  B  0.266667  0.333333   0.400
2  C  0.291667  0.333333   0.375

Changing the column value1 and the like to your headers should work similarly.