Use
RUN apt-get install -y python3-pip
That will work.
My test Dockerfile:
FROM ubuntu:20.04
RUN apt-get update
RUN apt-get upgrade -y
RUN apt-get install -y python3-pip
CMD tail -f /dev/null
# docker images
REPOSITORY TAG IMAGE ID CREATED SIZE
pip-test 0.1 1dd1ea8809d7 17 seconds ago 388MB
# docker run -d pip-test:0.1
docker exec -it b0ea8afe6bbd /bin/bash
root@b0ea8afe6bbd:/# pip3
Usage:
pip3 <command> [options]
Commands:
install Install packages.
...