24/7 live support would mean you only provide live support and no emails/telephone/tickets will be accepted and you dont provide a KB.
24/7 support means you can provide support by email, KB, phone, tickets, Live chat ETC.
It does not necessarily mean this exactly. From customer's point of view, live support often is a girl they can call to yell at, while their nameservers are propagating and website is down. Poor lass does not even have a right to respond, she must sit and listen to their lamentations. And if she is able so sooth their frustration and explain propagation cannot be influenced in any way - this is a great support then.
Knowledgebases are good, but customers are usually too lazy to read these. They prefer writing long and nervous tickets with bluster and words in caps, than surfing a well-organized knowledgebase with clear instructions and screenshots. They do not want to waste time (5-10 minutes) looking for answers themselves and prefer waiting for several hours or days to get a response from support instead. Ugly truth this is.
In terms of support (as for me) - hosting provider should be able to answer questions regarding any aspects of their service, whether these concern sales, setting up, billing, maintenance, backup or anything else. Majority of people prefer live communication, live chats at least, so knowledgebase is good... but not sufficient as source of support.
The things that really matter for me when choosing a hosting partner are:
uptime guarantee
service quality
support availability
costs
features offered
This list differs for everyone, of course.