probability - Representing 1/60 chance over 1,000 or 10,000 years?

If I have a an annual probability of $4.6 \times 10^{-4}$ and I'm evaluating that over a span of $35$ years can I multiply them together and get the probability of the event occurring with the $35$ year span?

If yes, it equals about $1/60$ chance (or $1.6$% chance). How can I represent that chance occurring per $1,000$ or $10,000$ years?