If the PM loses a vote of confidence he must ask the Governor General to drop the writ for a new general election. Theoretically the Governor General could decide that the Leader of Her Majesty's Loyal Opposition has a good chance of gaining and keeping the confidence of the house and so refuse to drop the writ and instead appoint the opposition leader as prime Minister. This is one of the so-called 'reserve powers" of the Governor General. The parties opposition parties seem to be relying on this fact.
But it is by no means certain that the Governor General would actually refuse to drop the writ. Since the King-Byng Wind-Ding in 1926, the conventional thinking is that the Governor General will never again hand over power to an opposition leader against the wishes of the Government but will always, instead, put the issue to the electorate in the form of a general election.
But this is matter of constitutional convention, not one of a "written constitution" so-called. A constitutional convention is not something that can be decided by a Court, instead it is something that is generally agreed to be the binding convention.
The question is whether the Governor General, who is a former Mother Corp personality appointed by a former Liberal government, will abide the convention or will instead again assert her "reserve powers" and thereby start a new convention (possibly at the risk of being condemned for acting as if she were an absolute monarch instead of as a constitutional fiction).
I am grossly over-simplifying and am explaining it badly. Canada's constitution is a mix of constitutional documents, statutes and unwritten conventional practices going back through time to Magna Charta. It is hard for one raised in it to interpret it to those raised in a theoretically wholly written constitution.