Convert/replace time from epoch milliseconds to human readable date in logfiles

I have a log file with the following structure

1522693524403 entity1,sometext
1522693541466 entity2,sometext
1522693547273 entity1,sometext
...

Now I would like to replace the time from epoch milliseconds to DD.MM.YYYY HH:MM:SS in all of the log files with a bash command on a Debian System. I tried different solutions provided here and on other websites but it did not really work for me.