UK Question: What is the statistical probability of being caught without a TV licence and being fined?

A great deal depends on your particular situation. I have never owned a television or (obviously) had a licence. Neither has anyone ever bothered me at my address so rubbish to say that 'any address with no licence is targeted'. They sent me a letter once which I answered saying I did not own a television. Peace and quiet since then (40 years). I am in central London btw.

Your biggest risk is that the prior tenant had a licence. When a flat with a licence suddenly does not have one, they start dribbling at the BBC. If you have cable tv or a dish, you are 100% guaranteed to get nailed.

UPDATE: With reference to your further question; you are quite right in that even under current rules you need to be watching live broadcasts although now these can be on a BBC player on your laptop rather than just through a television. However, if there is a communal sitting room with a television that is hooked up to receive broadcasts, then that is defacto evidence of a violation. The person who owns the television will be responsible for paying the licence fee. So that will be your landlord.

However, if your leases say that you are responsible for things like tv licences, your landlord will simply turn around and bill all of you for both the licence and the fine.

Very high, it is sensible not to chance it
Same with Cat licences
Their Detector Vans are highly sensitive
They can detect a Purr from 50 yards
Our Eric, being such a happy Cat was a piece of cake for them

They know who has a tv with no licence so the probability of being caught is high.
The best way to avoid this is to move house and live in the Catholic Falls road in Belfast, as tv licence inspectors are threatened with death if they enter the area, and the authorities feel it's best to just "overlook" this small area.

Quite high.
They check addresses with no license listed.
These are a very small number of houses so not hard to check.
No big vans needed these days.

Very high. They target addresses where no licence is registered and also addresses where new TVs have been bought. Stores have to tell the licensing authority of such transactions.