You asked
Is the sony rx100 iii good in low light?
Not really, at least not compared with bigger cameras. The RX100 III has a 1-inch sensor, which is smaller than APS-C and full frame, and small sensors gather less light and get noisier as ISO rises. Its lens is bright at the wide end (f/1.8), but it drops to f/2.8 when zoomed in, so you won't get much low-light help from the telephoto side. Its stabilisation does help with handheld shots in dim rooms.
If low light is the main job, look at the Sony a6400 for a larger APS-C sensor, paired with stabilised lenses since it has none in the body. For the best low-light results, the Sony a7S III is built for it, though its 12.1 megapixels make it a video camera first. The sensor guide explains why sensor size matters so much here.
Written by Claude from this site's pages.