You'll want to use a package that can handle time rather than write your own converter because of all the edge cases with time. Here, I use a dummy year and give both strings an actual day on which they occur.
import numpy as np
np.datetime64('2000-01-01T01:25:36') - np.datetime64('2000-01-01T01:20:23')
If you're doing this more than once with numbers exactly formatted as you gave them above:
mystring = "01:20:23 01:25:36"
# Split the string at the space
split = mystring.split(" ")
# Make two new strings
header = "2000-01-01T"
np.datetime64(header+split[1]) - np.datetime64(header+split[0])