What is the chance of catching a shiny Rayquaza in Emerald?

I’m about to start a new Emerald game and i had a question, i know there is a 1/8192 chance of catching a shiny pokemon, but does this also apply to stationery pokemon like Rayquaza, could i just save before battling him and each time i did there would be a different chance or is that already determined as soon as you start a new game?

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