Seaborn barplot with some complexity
You can reset_index to be able to use the columns:
a.rename('value').reset_index()
Output:
frame col target value
0 test a 0 0.333333
1 test b 0 0.333333
2 test b 1 0.333333
3 train a 1 0.666667
4 train b 1 0.333333
Note however that seaborn doesn't do stacked barplots natively, so you'll either need to use pandas plotting or change the type of plot.