How to validate idea if potential market is very small (high ticket)

So here's the situation:

I've identified a problem that is a very large scale (costs companies potentially $xx,xxx,xxx/year), can be partially solved (20-30%, possibly up to 50-60%), I know who my clients would be, and I can solve it (to the % outlined above). It's not easy or simple, but i have some ideas on how I can approach it.

The problem comes with validation - all of my potential clients are very big companies - in the $x,xxx,xxx,xxx range if not more. So the question is - how do I...

How to validate idea if potential market is very small (high ticket)

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