Well, according to Royal commentator Christine Ross, not very long at all.
"I really think they can't wait too long," Ms Ross told CBC.
"When you think about it, no matter who is there, the midwives might mention it to their husbands who tells their friend at football practice whose cousin happens to be a Daily Mail reporter and then it's everywhere.
"They really know that they don't have a ton of time to keep this to themselves because you never know what sort of comments, what sort of signal is going to let the world know 'oh, actually, this has happened."
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She continued: "God forbid Harry cancels an engagement because the baby is actually here, we're all going to start speculating and then the news is out.
"I think they have enough experience in their roles, Harry has experience in his role as royalty, that they can take some time to themselves but at the end of the day they can't keep that close for days or weeks on end."
