So if you have private Policing companies ....Would they be regulated or not?
Yes.
And if regulated, then by who?
The government, just like any other business.
And who awards the contracts.
The customers. It would work by customers paying $100/year for policing services from the company of their choice. Then if the customer gets murdered, raped, or have any other crime committed against them, they can call their private company number and the company can arrest someone with due process.
And just maybe, the poor conviction rate is not the fault of poor Policing, but perhaps has something to do with the legal system and it's private practitioners.
The poor conviction rate is largely because of the government being slow like it is with everything else. The private sector can do justice faster and better than the government.