According to the internet Singapore has one of the lowest crime rates in the world. The prison population may reflect a sentencing policy where people convicted of relatively minor offences are sent to prison. If that is so then the prison population cannot really be compared with the UK where every effort is made not to send people to prison, or to release them ASAP.
As for the miscarriages of justice you quote. Where do you get your figures which you rely upon ? The fact that people get acquitted on appeal does not necessarily mean they were wrongly convicted.