What is the difference between risk, uncertainty and ambiguity I am trying to pin down the difference between risk, uncertainty and ambiguity. 

As I understand, when behavioral economists talk about choice under uncertainty, they mean choice when agents face risk (known probability distribution over a range of outcomes) versus ambiguity (unknown probability distribution). So uncertainty is a blanket concept that can be broken down into risk and ambiguity. See for example Dannenberg et al (2014).

I also understand there is a debate on the meaning of these terms going back to Knight (1921) and Ellsberg (1961). Are there any competing definitions to the one above?
Here is a decision-theoretic formalization of your definitions.

The usual framework to talk about objective risk is the situation where a decision-maker expresses preferences over objective lotteries. Formally, if $X$ is a prize space, objective lotteries are defined as elements of the space $\Delta(X)$ of probability distributions (usually with finite support) over $X$. For instance, the decision-maker might be asked to form preferences between the lottery that offers her/him an apple with probability 0.3 and an orange with probability 0.7, and the lottery that offers her/him an apple with probability 0.5 and an orange with probability 0.5. The standard result in that area (von Neumann-Morgenstern theorem) delivers a representation that identifies the agent's attitude towards objective risk (her/his utility function), while the probabilities are given as a primitive of the model.

The usual framework to talk about ambiguity is the situation where a decision-maker expresses preferences over uncertain acts. Formally, if $X$ is a prize space and $S$ is a state space, acts are mappings $f:S \rightarrow X$ from $S$ to $X$. For instance, the decision-maker might be asked to form preferences between the act that offers her/him an apple if Novak Djokovic wins the 2017 Australian Open and an orange otherwise, and the lottery that offers her/him an apple if Andy Murray wins the 2017 Australian Open and an orange otherwise. The standard result in that area (von Neumann-Morgenstern theorem) delivers a representation that identifies both the agent's probabilistic beliefs regarding the states and her/his attitude towards risk (her/his utility function).

There is a third widely used concept, usually called Anscombe-Aumann acts or horse races, which associates both objective lotteries and uncertain acts. Formally, given a prize space $X$, an Anscombe-Aumann act is a mapping $f:S \rightarrow \Delta(X)$ that associates an objective lottery to any state in $S$.

Notice that the definitions of objective risk and ambiguity are to some extent subjective. The fact that risk is called "objective" relies very much on the assumption that the decision-maker agrees with the underlying probability model. For instance, if you observe the outcome of a coin toss, you might believe that heads happen with an objective probability of 0.5. It is implicitly imposed in the theory that the decision-maker agrees with this statement.

Regarding ambiguity, you might yourself believe that the act "receive an apple if Novak Djokovic wins the 2017 Australian Open" is very ambiguous because you have no idea on how to compute a subjective probability for this event. That said, another decision-maker might very confidently believe that Djokovic has a 74% chance of winning the tournament, in which case she/he does not perceive this act as ambiguous at all. Ambiguity is a subjective notion, which is given by people's preferences and behavior and not by the choice situation itself.