I think the problem is that there isn't any shower base to speak of - it's just tiled. Maybe they aren't sealed, and the water is leaking through the grout (or mortar, or whatever that stuff is between the tiles). Can you tell I'm not a handyman !!!
About the cost - I told the Real Estate agent, who is the most unapproachable, arrogant
pr!ck that I've ever dealt with, that there was moisture present, and there is proof a water damage on the kitchen ceiling. He rang back to say the owner will get a quote to fix the problem. I'll insist on being there to see what work is actually carried out, and to make sure that the work is covered by a written guarantee. I think the guarantee is standard practice for leaking showers.
Peter - your engineering logic comes through loud and clear