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The actual mathematical odds the devs coded into each item are not known. In my personal experience, the higher value of the prize, the more items you'll have to open to get it.
For the 3* scratch ticket on the golden fleece, it is however much more frequent (since you win with the fragments and not the 3* prizes). I actually get 3* tickets more frequently than 2*, with 1* tickets remaining the most frequent. I don't know for other players though.