What is the relation between probability of default and country's interest rates? Is probability of default expected to increase with increase in the interest rates set by the central bank?
The answer depends on the situation for the country in question. Since the answer is correspondingly very large if we covered all cases, I am only attempting to offer an overview of the cases. Feel free to ask follow up questions on more specific questions.

I will cover three important sinplified cases.


“Gold Standard”/“hard currency borrowing”.
Free-floating fiat currency.
Euro area.


(1) The “gold standard” example is not currently of interest, but if you want to look at historical governmental defaults, they were associated with the gold standard, or the countries borrowing in a foreign currency (“hard currency”). (Countries in currency pegs are also in a similar situation.)

In a gold standard, the government’s money in some sense can be converted into gold. Ultimately, it needs to have enough tax revenue in its local currency to force the private sector to turn in enough currency so that the consolidated government (fiscal arm/central bank) can honour the conversion parity. If that level of taxes is not politically sustainable, the government will be forced to default.

The usual operating procedure in a gold standard is for the central bank to raise interest rates to attract gold inflows. However, this raises the interest expense of the government, and so it makes it harder to sustain the gold parity price. So in this case, higher interest rates can raise default rates. However, the causality is ambiguous - the central bank is often forced to raise interest rates to defend the currency value, snd the currency is falling in value because of an expected default. Therefore, one could argue that high interest rates in a currency peg country are the result of an elevated default risk.

For countries with a currency peg or borrow in a foreign currency, they are in a similar boat, as they need to impose taxes in order to be able to obtain the external instrument.

(2) A floating currency sovereign (e.g. the United States, the United Kingdom, Japan, Canada...) does not attempt to fix the value of its currency versus external instruments. It can create arbitrary amounts of its currency unit without using any real resources. The only real concern is the purchasing power of the currency unit (inflation).

Since there are no external constraints (lack of gold), default is essentially a political decision. 


There are operating procedures that might entail default (e.g. the debt ceiling in the United States). It is a political decision to not override those procedures.
Interest spending may be such a high part of the budget that politicians would rather default than pay the interest.
Government debt may be viewed as illegitimate. For example, debts incurred by a radical government that was later overthrown.


High interest rates might help push a country towards default, but that was not the case in the 1970s. The number of defaults of countries in this situation is so low and usually associated with other problems that there are almost no data to draw conclusions from.

3) The euro area is a special case: the currency itself is a fiat currency, but it is under the control of a central bank that is a supranational entity. The euro area nations are not sovereign in the same sense that the federal Government of Canada is, rather they are in a situation similar to a Canadian province.