Much more complicated than it needs to be. You extend a list, then traverse the list to construct a counter, then traverse again to get a sorted sequence, then traverse again to get a list of keys only; this all needs to go away - especially the lambda/map style which is better expressed with comprehensions.
Instead, work with your Counter as a first-class citizen. Don't juggle indices. And spend some quality time reading the Counter documentation.
Suggested
import json
from collections import Counter
from pprint import pprint
with open('contributors_sample.json') as f:
contributors_file = json.load(f)
jobs = Counter()
for contributor in contributors_file:
jobs.update(contributor['jobs'])
print('Top jobs:', jobs.most_common(5))
for contributor in contributors_file:
top_freq, contributor['top_job'] = max(
(jobs[job], job)
for job in contributor['jobs']
)
pprint(contributors_file)
As a more direct and obscure alternative, the top_job assignment can be written as
contributor['top_job'] = max(
contributor['jobs'], key=jobs.__getitem__,
)