Add new column with number of occurences (.isin) in other column

Question

How can I count how often each value in the column substring occurs in the column string and append the result as a new column given this example dataframe:

df = pd.DataFrame({
'substring':['a', 'b', 'c', 'a', 'b', 'c', 'd', 'd', 'a']
'string':['a a b', '', 'a a', 'b', 'a b', 'a c a', '', 'b c a', 'd d']})

  substring string
0         a  a a b
1         b      
2         c    a a
3         a      b
4         b    a b
5         c  a c a
6         d       
7         d  b c a
8         a    d d

and here what I'd like the output to look like:

  substring string count
0         a  a a b    5
1         b           4
2         c    a a    2
3         a      b    5
4         b    a b    4
5         c  a c a    2
6         d           1
7         d  b c a    1
8         a    d d    5