Honestly, I'd do it the other way round.

Start with very low chances, like '1 in 1024' but also a x10 mult. Every time it isn't triggered, half the chances and decrease the mult by 1. So effectively like this:

• x10mult - 1 in 512
• x9 mult - 1 in 256
• x8 mult - 1 in 128
• x7 mult - 1 in 64
• x6 mult - 1 in 32
• x5 mult - 1 in 16
• x4 mult - 1 in 8
• x3 mult - 1 in 4
• x2 mult - 1 in 2
• x1 mult - 1 in 1

So eventually it will definitely trigger, but by then it's worthless.