Handbrake is free and popular software solution for video converting.https://handbrake.frhttps://en.wikipedia.org/wiki/HandBrake
Here you can find free alternatives if you're not satisfied:https://alternativeto.net/software/handbrake
Keep in mind that some of .ts files have copyright protection so they can be played only on exact tv set or set-top-box(receiver) where they are recorded, and if that's the case, then also can't be converted to other playable formats.
I had a problem with playing recorded .ts file from my tv set on friends' same model of tv set. Copyright protection was connected with serial number of each tv set.