Heh. So it turns out, figuring out the answer to this is precisely what I do for a living.

The glib answer: it depends.

1. It depends on how big an object you are worried about hitting. Are you worried about damaging wiring harnesses? Are you worried about causing a radiator leak? Punching a hole in the crew module? Annihilating the vehicle altogehter? The larger the object, the less likely, in rather dramatic scale.
2. It depends on what orbit you fly in. Different altitudes and inclinations have drastically different debris populations.
3. It depends on how big your vehicle is. Bigger vehicles get hit more.
4. It depends on how long you fly. Stay in orbit 10 years, and you'll get hit with roughly 10 times as much stuff as you would if you stayed for one year.

On ISS, we typically write requirements along these lines:

The [piece of hardware] will not sustain damage from orbital debris that could create
a [catastrophic hazard | subcomponent failure | other defined failure] with a probability 
of 0.xyz over XY years.

What exactly we write depends specifically on the hardware involved, how much we care about it, how much could station suffer if we lost it, etc.

New piece of critical structure? We'd specify a pretty stringent requirement, say, something more than 99% over a decade.

Wire harness for a wifi antenna for payloads? Maybe not so much, say, 95-98% per year.

A more stringent requirement makes the hardware and (and perhaps more importantly) its certification process more expensive.

Heh. So it turns out, figuring out the answer to this is precisely what I do for a living.

The glib answer: it depends.

1. It depends on how big an object you are worried about hitting. Are you worried about damaging wiring harnesses? Are you worried about causing a radiator leak? Punching a hole in the crew module? Annihilating the vehicle altogether? The larger the object, the less likely, in rather dramatic scale.
2. It depends on what orbit you fly in. Different altitudes and inclinations have drastically different debris populations.
3. It depends on how big your vehicle is. Bigger vehicles get hit more.
4. It depends on how long you fly. Stay in orbit 10 years, and you'll get hit with roughly 10 times as much stuff as you would if you stayed for one year.

On ISS, we typically write requirements along these lines:

The [piece of hardware] will not sustain damage from orbital debris that could create a [catastrophic hazard | subcomponent failure | other defined failure] with a probability of 0.xyz over XY years.

What exactly we write depends specifically on the hardware involved, how much we care about it, how much could station suffer if we lost it, etc.

New piece of critical structure? We'd specify a pretty stringent requirement, say, something more than 99% over a decade.

Wire harness for a Wi-Fi antenna for payloads? Maybe not so much, say, 95-98% per year.

A more stringent requirement makes the hardware and (and perhaps more importantly) its certification process more expensive.