This is a big, big question that can be answered from many different sides. First I want to point you to some previous answers on the site that are relevant to your question but don't directly answer it:

• Why is Africa not as developed as the other continents besides Antarctica?
• /u/khosikulu's answer to Why are former African colonies generally much less developed than former Asian colonies?
• Why did all of the other continents develop so much quicker than Africa?

So some of it is that ideas about prosperity and advancement are culturally bound and historically contingent. Some of it is down to geographical factors. A whole lot of it is due to a Euro-American tendency to collapse all of Africa into a stereotype of the famished child while ignoring Ghanaian engineering capabilities or the cultural output of Nollywood.

I'd like to add to those previous answers by arguing that the different outcomes for the former colonies you mentioned is largely due to the fact that the British Empire had two different types of colonies, and they treated those colonies differently!

We can break imperial strategies into two broad types*:

1. settler colonial projects (represented in your question by Australia and Canada), and
2. extractive/trading projects (represented by British African colonies).

*It's helpful to think about these two types as totally separate entities,, but there's actually quite a bit of overlap in the details.

Let's start with Type 2 (extractive/trading projects). In Type 2 colonies like the Gold Coast (today's Ghana), Jamaica, and India, it was understood that a very small number of white British authority figures--soldiers, sailors, missionaries, traders--would need to maintain control over an overwhelmingly "native" population. To do this, imperial powers used an array of tactics including inciting unrest among local ethnic groups to divide and conquer; coercing or cajoling local political leaders into collaboration; undercutting local economies; and using straight-up violence. The goal of this type of colony was to suck as much money/commodities/trading opportunities as possible out of the colony and send the proceeds back to Britain. Britain valued Type 2 colonies for the riches they provided, but the well-being of Amari the fishmonger of Zanzibar was emphatically not a priority.

In Type 1 projects like Australia, New Zealand, and Canada (and, to an extent, parts of southern African colonies), the emphasis was on displacing/exterminating Indigenous people, and sending in emigrants from the British Isles who would stay (semi-)permanently and establish a society in line with British mores. In the settler colonies, emigrants were empowered to set up local governments according to the British models they left behind. (Because emigrants to settler colonies were usually British Protestants, they were assumed to be generally capable of responsibly governing on a local level.) And because Britain had stronger religious, cultural, and familial ties to the settler projects than to the extractive/trading projects, Britain had more of an interest in ensuring the well-being (read: political and economic stability) of the emigrants than they did in setting up the non-white extractive colonies. Angela Woollacott has shown how the cultivation of these affective, political, cultural, and economic ties between Britain and its settler colonies led white Australians to frequently view Britain as "home," even when they had never been there.

tl;dr Britain had two main categories of colonies. The colonies you mention as prosperous were Type 1 (the type governed with less coercion). The colonies you mention as "in shambles" were Type 2 (the type more explicitly exploited and ruled with violence). British attitudes toward the colonies affected the styles of rule applied to each colony, and these styles of rule have had compounding effects even post-"independence."