Number timestamped rows

Dear all,
maybe a stupid question, but: I have a table that is ordered like this:

user_id|timestamp|event
1 |0:1 |event_a
1 |0:2 |event_b
2 |0:1 |event_b
2 |0:3 |event_c
2 |0:4 |event_b
3 |0:1 |event_a

and I would like to number them according to their timestamps like this:

user_id|timestamp|event |order
1 |0:1 |event_a |1
1 |0:2 |event_b |2
2 |0:1 |event_b |1
2 |0:3 |event_c |2
2 |0:4 |event_b |3
3 |0:1 |event_a |1

How would I do this with an UPDATE statement (e.g.) in pgsql?

Thanks in advance for any hint
Jan

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